{"id":37832,"date":"2019-02-15T10:14:21","date_gmt":"2019-02-15T10:14:21","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=37832"},"modified":"2020-11-19T19:24:35","modified_gmt":"2020-11-19T13:54:35","slug":"plus-two-maths-chapter-wise-questions-answers-chapter-3","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/","title":{"rendered":"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices"},"content":{"rendered":"

Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices are part of Plus Two Maths Chapter Wise Questions and Answers<\/a>. Here we have given Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices.<\/p>\n\n\n\n\n\n\n\n\n\n\n
Board<\/strong><\/td>\nSCERT, Kerala<\/td>\n<\/tr>\n
Text Book<\/strong><\/td>\nNCERT Based<\/td>\n<\/tr>\n
Class<\/strong><\/td>\nPlus Two<\/td>\n<\/tr>\n
Subject<\/strong><\/td>\nMaths\u00a0Chapter Wise Questions<\/td>\n<\/tr>\n
Chapter<\/strong><\/td>\nChapter 3<\/td>\n<\/tr>\n
Chapter Name<\/strong><\/td>\nMatrices<\/td>\n<\/tr>\n
Number of Questions Solved<\/strong><\/td>\n39<\/td>\n<\/tr>\n
Category<\/strong><\/td>\nPlus Two Kerala<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Kerala Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices<\/h2>\n

Plus Two Maths Matrices Three Mark Questions and Answers<\/h3>\n

Question 1.
\nFind the value of a, b and c from the following equations;
\n\\(\\left[\\begin{array}{cc}{a-b} & {2 a+c} \\\\{2 a-b} & {3 c+d}
\n\\end{array}\\right]=\\left[\\begin{array}{cc}{-1} & {5} \\\\{0} & {13}\\end{array}\\right]\\).
\nAnswer:
\nGiven;
\n\\(\\left[\\begin{array}{cc}{a-b} & {2 a+c} \\\\{2 a-b} & {3 c+d}
\n\\end{array}\\right]=\\left[\\begin{array}{cc}{-1} & {5} \\\\{0} & {13}\\end{array}\\right]\\)
\n\u21d2 a – b = -1, 2a + c = 5, 2a – b = 0, 3c + d = 13
\n\u21d2 a – b = -1
\n2a – b = 0<\/span>
\n– a = -1
\n\u21d2 a = 1
\nWe have, a – b = -1 \u21d2 1 – b = -1 \u21d2 b = 2
\n\u21d2 2a + c = 5 \u21d2 2 + c = 5 \u21d2 c = 3
\n\u21d2 3c + d = 13 \u21d2 9 + d = 13 \u21d2 d = 4.<\/p>\n

Question 2.
\nSimplify cosx\\(\\left[\\begin{array}{cc}{\\cos x} & {\\sin x} \\\\{-\\sin x} & {\\cos x}\\end{array}\\right]\\) + sinx\\(\\left[\\begin{array}{cc}{\\sin x} & {-\\cos x} \\\\{\\cos x} & {\\sin x}\\end{array}\\right]\\).
\nAnswer:
\n\"Plus<\/p>\n

Question 3.
\nSolve the equation for x, y z and t; if
\n\\(2\\left[\\begin{array}{ll}{x} & {z} \\\\{y} & {t}\\end{array}\\right]+3\\left[\\begin{array}{cc}{1} & {-1} \\\\{0} & {2}\\end{array}\\right]=3\\left[\\begin{array}{ll}{3} & {5} \\\\{4} & {6}\\end{array}\\right]\\).
\nAnswer:
\n\"Plus
\n\u21d2 2x + 3 = 9 \u21d2 x = 3
\n\u21d2 2z – 3 = 15 \u21d2 z = 9
\n\u21d2 2y = 12 \u21d2 y = 6
\n\u21d2 2t + 6 = 18 \u21d2 t = 6.<\/p>\n

Question 4.
\nFind A2<\/sup> – 5A + 6I If A = \\(\\left[\\begin{array}{ccc}{2} & {0} & {1} \\\\{2} & {1} & {3} \\\\{1} & {-1} & {0}\\end{array}\\right]\\)
\nAnswer:
\n\"Plus
\nA2<\/sup> – 5A + 6I
\n\"Plus<\/p>\n

Question 5.
\nIf A = \\(\\left[\\begin{array}{cc}{3} & {-2} \\\\{4} & {-2}\\end{array}\\right]\\) find k so that A2<\/sup> = kA – 2I.
\nAnswer:
\n\"Plus
\nGiven A2<\/sup> = kA – 2I
\n\"Plus
\n1 = 3k – 2
\n\u21d2 k = 1.<\/p>\n

Question 6.
\nExpress A = \\(\\left[\\begin{array}{ccc}{-1} & {2} & {3} \\\\{5} & {7} & {9} \\\\{-2} & {1} & {1}
\n\\end{array}\\right]\\) as the sum of a symmetric and skew symmetric matrix.
\nAnswer:
\n\"Plus
\nP = 1\/2 (A + AT<\/sup>) is symmetric.
\nQ = 1\/2 (A – AT<\/sup>) is skew symmetric.
\n\"Plus<\/p>\n

Question 7.
\nFind the inverse of the following using elementary transformations.
\n\"Plus
\nAnswer:
\n(i) Let A = I A
\n\"Plus<\/p>\n

(ii) Let A = IA
\n\"Plus<\/p>\n

(iii) Let A = IA
\n\"Plus<\/p>\n

(iv) Let A = IA
\n\"Plus<\/p>\n

Question 8.
\nFind the inverse of the matrix A = \\(\\left[\\begin{array}{cc}{2} & {3} \\\\{-1} & {5}\\end{array}\\right]\\) using row transformation.
\nAnswer:
\nA = \\(\\left[\\begin{array}{cc}{2} & {3} \\\\{-1} & {5}\\end{array}\\right]\\)
\nLet A = IA
\n\"Plus<\/p>\n

Question 9.
\n\\(A=\\left[\\begin{array}{ll}{2} & {3} \\\\{4} & {5} \\\\{2} & {1}\\end{array}\\right] B=\\left[\\begin{array}{ccc}{1} & {-2} & {3} \\\\{-4} & {2} & {5}\\end{array}\\right]\\)<\/p>\n

    \n
  1. Find AB<\/li>\n
  2. If C is the matrix obtained from A by the transformation R1<\/sub> \u2192 2R1<\/sub>, find CB<\/li>\n<\/ol>\n

    Answer:
    \n\"Plus<\/p>\n

    (ii) Since C is the matrix obtained from A by the transformation R1<\/sub> \u2192 2R1<\/sub>
    \n\u21d2 C = \\(\\left[\\begin{array}{ll}{4} & {6} \\\\{4} & {5} \\\\{2} & {1}\\end{array}\\right]\\)
    \nThen CB can be obtained by multiplying first row of AB by 2.
    \nCB = \\(\\left[\\begin{array}{ccc}{-20} & {-4} & {42} \\\\{-16} & {2} & {37} \\\\{-2} & {-2} & {11}
    \n\\end{array}\\right]\\).<\/p>\n

    Question 10.
    \nConstruct a 3 \u00d7 4 matrix whose elements are given by<\/p>\n

      \n
    1. ay<\/sub> = \\(\\frac{|-3 i+j|}{2}\\) (2)<\/li>\n
    2. aij<\/sub> = 2i – j (2)<\/li>\n<\/ol>\n

      Answer:
      \n\"Plus
      \na13<\/sub> = 0, a14<\/sub> = \\(\\frac{1}{2}\\), a21<\/sub> = \\(\\frac{5}{2}\\), a22<\/sub> = 2, a23<\/sub> = \\(\\frac{3}{2}\\), a24<\/sub> = 1, a31<\/sub> = 4, a32<\/sub> = \\(\\frac{7}{2}\\), a33<\/sub> = 3, a34<\/sub> = \\(\\frac{5}{2}\\)
      \n\"Plus<\/p>\n

      \"Plus
      \na11<\/sub> = 1, a12<\/sub> = 0, a13<\/sub>= -1, a14<\/sub> = -2, a21<\/sub> = 3, a22<\/sub> = 2, a23<\/sub> = 1, a24<\/sub> = 0, a31<\/sub> = 5, a32<\/sub> = 4, a33<\/sub> = 3, a34<\/sub> = 2
      \n\"Plus<\/p>\n

      Question 11.
      \nExpress the following matrices as the sum of a Symmetric and a Skew Symmetric matrix.
      \n(i) \\(\\left[\\begin{array}{ccc}{6} & {-2} & {2} \\\\{-2} & {3} & {-1} \\\\{2} & {-1} & {3}
      \n\\end{array}\\right]\\)
      \n(ii) \\(\\left[\\begin{array}{ccc}{3} & {3} & {-1} \\\\{-2} & {-2} & {1} \\\\{-4} & {-5} & {2}
      \n\\end{array}\\right]\\)
      \nAnswer:
      \n\"Plus<\/p>\n

      \"Plus<\/p>\n

      \"Plus<\/p>\n

      \"Plus<\/p>\n

      Question 12.
      \nIf A = \\(\\left[\\begin{array}{ccc}{2} & {4} & {3} \\\\{1} & {0} & {6} \\\\{0} & {-2} & {-3}\\end{array}\\right]\\)<\/p>\n

        \n
      1. Find 3A. (1)<\/li>\n
      2. Find AT<\/sup> (1)<\/li>\n
      3. Evaluate A + AT<\/sup> , is it symmetric? Justify your answer. (1)<\/li>\n<\/ol>\n

        Answer:
        \n1. 3A = \\(\\left[\\begin{array}{ccc}{6} & {12} & {9} \\\\{3} & {0} & {18} \\\\{0} & {-6} & {-9}
        \n\\end{array}\\right]\\)<\/p>\n

        2. AT<\/sup> = \\(\\left[\\begin{array}{ccc}{2} & {1} & {0} \\\\{4} & {0} & {-2} \\\\{3} & {6} & {-3}
        \n\\end{array}\\right]\\)<\/p>\n

        3. A + AT<\/sup>
        \n\"Plus
        \nThe elements on both sides of the main diagonal are same. Therefore A + AT <\/sup>is a symmetric matrix.<\/p>\n

        Plus Two Maths Matrices Four Mark Questions and Answers<\/h3>\n

        Question 1.
        \nConsider the following statement: P(n) : An<\/sup> = \\(\\left[\\begin{array}{cc}{1+2 n} & {-4 n} \\\\{n} & {1-2 n}\\end{array}\\right]\\) for all n \u2208 N<\/p>\n

          \n
        1. Write P (1). (1)<\/li>\n
        2. If P(k) is true, then show that P( k + 1) is also true. (3)<\/li>\n<\/ol>\n

          Answer:
          \n1. P(1) : A = \\(\\left[\\begin{array}{cc}{1+2} & {-4} \\\\{1} & {1-2}\\end{array}\\right]=\\left[\\begin{array}{cc}{3} & {-4} \\\\{1} & {-1}\\end{array}\\right]\\)<\/p>\n

          2. Assume that P(n) is true n = k
          \n\"Plus
          \nHence P(k+1) is true n \u2208 N.<\/p>\n

          Question 2.
          \nFind the matrices A and B if 2A + 3B = \\(\\left[\\begin{array}{ccc}{1} & {2} & {-1} \\\\{0{1} & {2} & {4}\\end{array}\\right]\\) and A + 2B = \\(\\left[\\begin{array}{lll}{2} & {0} & {1} \\\\{1} & {1} & {2} \\\\{3} & {1} & {2}\\end{array}\\right]\\).
          \nAnswer:
          \n\"Plus
          \nSolving (1) and (2) \u21d2 2 \u00d7 (2)
          \n\"Plus<\/p>\n

          \"Plus
          \nQuestion 3.<\/p>\n

            \n
          1. Construct a 3 \u00d7 3 matrix A = [aij<\/sub>] where aij<\/sub> – 2(i – j) (3)<\/li>\n
          2. Show that matrix A is skew-symmetric. (1)<\/li>\n<\/ol>\n

            Answer:
            \n1.
            \n\"Plus<\/p>\n

            2.
            \n\"Plus
            \nTherefore A is a skew-symmetric matrix.<\/p>\n

            Question 4.
            \nConsider the following statement P(n ): An<\/sup> = \\(\\left[\\begin{array}{cc}{\\cos n \\theta} & {\\sin n \\theta} \\\\{-\\sin n \\theta} & {\\cos n \\theta}\\end{array}\\right]\\) for all n \u2208 N<\/p>\n

              \n
            1. Write P(1). (1)<\/li>\n
            2. If P (k) is true then show that P (k+1) is true (3)<\/li>\n<\/ol>\n

              Answer:
              \n1.
              \n\"Plus<\/p>\n

              2. Assume that P(n) is true for n = k
              \n\"Plus
              \nP(k+1) = Ak+1<\/sup>
              \n\"Plus
              \n\u2234 P(k+1) is true. Hence true for all n \u2208 N.<\/p>\n

              Question 5.
              \nA = \\(\\left[\\begin{array}{lll}{1} & {2} & {2} \\\\{2} & {1} & {2} \\\\{2} & {2} & {1}\\end{array}\\right]\\), then<\/p>\n

                \n
              1. Find 4A and A2<\/sup> (2)<\/li>\n
              2. Show that A2<\/sup> -4A = 5I3<\/sub> (2)<\/li>\n<\/ol>\n

                Answer:
                \n1.
                \n\"Plus<\/p>\n

                2.
                \n\"Plus<\/p>\n

                Question 6.
                \nLet A = \\(\\left[\\begin{array}{lll}{2} & {1} & {3} \\\\{4} & {1} & {0}\\end{array}\\right]\\) and B= \\(\\left[\\begin{array}{cc}{1} & {-1} \\\\{0} & {2} \\\\{5} & {0}\\end{array}\\right]\\)<\/p>\n

                  \n
                1. Find AT<\/sup> and BT<\/sup> (1)<\/li>\n
                2. Find AB (1)<\/li>\n
                3. Show that (AB)T<\/sup> = BT<\/sup> AT<\/sup> (2)<\/li>\n<\/ol>\n

                  Answer:
                  \n1.
                  \n\"Plus<\/p>\n

                  2.
                  \n\"Plus<\/p>\n

                  3.
                  \n\"Plus
                  \n\u2234 (AB)T<\/sup> = BT<\/sup> AT<\/sup>.<\/p>\n

                  Question 7.
                  \nA = \\(\\left[\\begin{array}{ccc}{1} & {-3} & {1} \\\\{2} & {0} & {4} \\\\{1} & {2} & {-2}\\end{array}\\right]\\) Express A as the sum of a symmetric and skew symmetric matrix.
                  \nAnswer:
                  \n\"Plus
                  \n\\(\\frac{1}{2}\\) (A + AT<\/sup>) + \\(\\frac{1}{2}\\) (A – AT<\/sup>)
                  \n\"Plus<\/p>\n

                  Question 8.<\/p>\n

                    \n
                  1. Consider a 2 \u00d7 2 matrix A = [aij<\/sub>], where aij<\/sub> = \\(\\frac{(i+j)^{2}}{2}\\)<\/li>\n
                  2. Write the transpose of A. (2)<\/li>\n
                  3. Show that A is symmetric. (2)<\/li>\n<\/ol>\n

                    Answer:
                    \n1. A = \\(\\left[\\begin{array}{ll}{2} & {\\frac{9}{2}} \\\\{\\frac{9}{2}} & {8}\\end{array}\\right]\\)<\/p>\n

                    2. AT<\/sup> = \\(\\left[\\begin{array}{ll}{2} & {\\frac{9}{2}} \\\\{\\frac{9}{2}} & {8}\\end{array}\\right]\\)<\/p>\n

                    3. AT<\/sup> = A therefore symmetric matrix.<\/p>\n

                    Question 9.
                    \nA = \\(\\left[\\begin{array}{ll}{6} & {5} \\\\{7} & {6}\\end{array}\\right]\\) is a matrix<\/p>\n

                      \n
                    1. What is the order of A. (1)<\/li>\n
                    2. Find A2<\/sup> and 12 A. (2)<\/li>\n
                    3. If f(x) = xT<\/sup> – 12x +1; find f(A). (1)<\/li>\n<\/ol>\n

                      Answer:
                      \n1. Order of A is 2 \u00d7 2.<\/p>\n

                      2.
                      \n\"Plus<\/p>\n

                      3. f(x) = x2<\/sup> – 12x + 1 \u21d2 f(A) = A2<\/sup> – 12A + I
                      \n\"Plus<\/p>\n

                      Plus Two Maths Matrices Six Mark Questions and Answers<\/h3>\n

                      Question 1.
                      \nLet A = \\(\\left[\\begin{array}{ll}{2} & {4} \\\\{3} & {2}\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{cc}{1} & {3} \\\\{-2} & {5}\\end{array}\\right]\\), C = \\(\\left[\\begin{array}{rr}{-2} & {5} \\\\{3} & {4}\\end{array}\\right]\\)
                      \nFind each of the following
                      \n(i) A + B; A – B
                      \n(ii) 3A – C
                      \n(iii) AB
                      \n(iv) BA
                      \nAnswer:
                      \n\"Plus<\/p>\n

                      \"Plus<\/p>\n

                      \"Plus<\/p>\n

                      \"Plus<\/p>\n

                      Question 2.
                      \nLet A = \\(\\left[\\begin{array}{ll}{1} & {2} \\\\{3} & {4}\\end{array}\\right]\\); B = \\(\\left[\\begin{array}{ll}{2} & {1} \\\\{4} & {5}\\end{array}\\right]\\); C = \\(\\left[\\begin{array}{ccc}{1} & {-1} \\\\{0} & {2}\\end{array}\\right]\\)
                      \n(i) Find A + B and A – B (2)
                      \n(ii) Show that (A + B) + C = A + (B + C) (2)
                      \n(iii) Find AB and BA
                      \nAnswer:
                      \n\"Plus<\/p>\n

                      \"Plus
                      \n\u2234 (A + B) + C = A + (B + C)
                      \n\"Plus<\/p>\n

                      Question 3.
                      \nA = \\(\\left[\\begin{array}{ccc}{-1} & {0} & {2} \\\\{4} & {0} & {-3}\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{cc}{0} & {2} \\\\{-1} & {3} \\\\{0} & {4}\\end{array}\\right]\\)<\/p>\n

                        \n
                      1. What is the order of matrix AB ? (1)<\/li>\n
                      2. Find AT<\/sup>, BT<\/sup> (2)<\/li>\n
                      3. Verify (AB)T<\/sup> = BT<\/sup> AT<\/sup> (3)<\/li>\n<\/ol>\n

                        Answer:
                        \n1. Order of AB is 2 \u00d7 2. Since order of A is 2 \u00d7 3 and B is 3 \u00d7 2.<\/p>\n

                        2.
                        \n\"Plus<\/p>\n

                        3.
                        \n\"Plus
                        \n(AB)T<\/sup> = BT<\/sup> AT<\/sup>.<\/p>\n

                        Question 4.
                        \nLet A = \\(\\left[\\begin{array}{rrr}{1} & {2} & {-3} \\\\{2} & {1} & {-1}\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{ll}{2} & {3} \\\\{5} & {4} \\\\{1} & {6}\\end{array}\\right]\\)
                        \n(i) FindAB. (1)
                        \n(ii) Find AT<\/sup>, BT<\/sup> & (AB)T<\/sup> (3)
                        \n(iii) Verify that (AB)T<\/sup> = BT<\/sup> AT<\/sup> (2)
                        \nAnswer:
                        \n\"Plus<\/p>\n

                        \"Plus<\/p>\n

                        \"Plus<\/p>\n

                        Question 5.
                        \nIf A = \\(\\left[\\begin{array}{c}{-2} \\\\{4} \\\\{5}\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{lll}{1} & {3} & {6}\\end{array}\\right]\\)
                        \n(i) Find AT<\/sup>, BT<\/sup> (1)
                        \n(ii) Find (AB)T<\/sup> (2)
                        \n(iii) Verify (AB)T<\/sup> = BT<\/sup> AT<\/sup> (3)
                        \nAnswer:
                        \n\"Plus<\/p>\n

                        \"Plus<\/p>\n

                        \"Plus<\/p>\n

                        Question 6.
                        \nLet A = \\(\\left[\\begin{array}{cc}{3} & {1} \\\\{-1} & {2}\\end{array}\\right]\\)
                        \n(i) Find A2<\/sup> (1)
                        \n(ii) Show that A2<\/sup> – 5A + 7I = 0 (1)
                        \n(iii) Using this result find A-1<\/sup> (2)
                        \n(iv) Slove the following equation using matrix: 3x + y = 1, – x + 2y = 2.
                        \nAnswer:
                        \n\"Plus<\/p>\n

                        \"Plus<\/p>\n

                        (iii) A2<\/sup> – 5A + 7I = 0 \u21d2 A2<\/sup> – 5A = -7I,
                        \nmultiplying by A-1<\/sup> on both sides,
                        \n\u21d2 A – 5I = -7 A-1<\/sup>
                        \n\"Plus<\/p>\n

                        (iv) The equation can be represented in matrix form as follows, AX = B \u21d2 X = A-1<\/sup>B
                        \n\"Plus<\/p>\n

                        Question 7.
                        \nA = \\(\\left[\\begin{array}{ccc}{1} & {2} & {3} \\\\{3} & {-2} & {1} \\\\{4} & {2} & {1}
                        \n\\end{array}\\right]\\)
                        \n(i) Show that A3<\/sup> – 23A – 40I = 0 (3)
                        \n(ii) Hence find A-1<\/sup> (3)
                        \nAnswer:
                        \n\"Plus
                        \nA3<\/sup> – 23A – 40I = 0
                        \n\"Plus<\/p>\n

                        (ii) A-1<\/sup>A3<\/sup> – 23 A-1<\/sup>A – 40A-1<\/sup>I = 0
                        \n\u21d2 A2<\/sup> – 23I – 40A-1<\/sup> = 0
                        \n\"Plus<\/p>\n

                        Question 8.
                        \nA is a third order square matrix and \\(a_{i j}=\\left\\{\\begin{aligned}-i+2 j & \\text { if } i=j \\\\i \\times j & \\text { if } i \\neq j\\end{aligned} \\text { and } B=\\left[\\begin{array}{lll}{2} & {1} & {1} \\\\{1} & {1} & {5} \\\\{1} & {5} & {2}\\end{array}\\right]\\right.\\)<\/p>\n

                          \n
                        1. Construct the matrix A. (1)<\/li>\n
                        2. Interpret the matrix A. (1)<\/li>\n
                        3. Find AB – BA. (3)<\/li>\n
                        4. Interpret the matrix AB – BA. (1)<\/li>\n<\/ol>\n

                          Answer:
                          \n1. a11<\/sub> = 1, a12<\/sub> = 2, a13<\/sub> = 3, a21<\/sub> = 2, a22<\/sub> = 2, a23<\/sub> = 6, a31<\/sub> = 3, a32<\/sub> = 6, a33<\/sub> = 3
                          \nA = \\(\\left[\\begin{array}{lll}{1} & {2} & {3} \\\\{2} & {2} & {6} \\\\{3} & {6} & {3}\\end{array}\\right]\\)<\/p>\n

                          2. Now,
                          \n\"Plus
                          \nTherefore A is symmetric matrix.<\/p>\n

                          3.
                          \n\"Plus<\/p>\n

                          \"Plus<\/p>\n

                          \"Plus<\/p>\n

                          4.
                          \n\"Plus
                          \n= -(AB – BA)
                          \n\u2234 skew symmetric matrix.<\/p>\n

                          Question 9.
                          \nFind x and y if
                          \n\"Plus
                          \nAnswer:
                          \n\"Plus<\/p>\n

                          \"Plus<\/p>\n

                          \"Plus<\/p>\n

                          \"Plus<\/p>\n

                          Question 10.
                          \nGiven that A + B = \\(\\left[\\begin{array}{ll}{2} & {5} \\\\{7} & {8}\\end{array}\\right]\\) and A – B = \\(\\left[\\begin{array}{ll}{6} & {8} \\\\{4} & {3}\\end{array}\\right]\\)<\/p>\n

                            \n
                          1. Find 2A. (1)<\/li>\n
                          2. Find A2<\/sup> – B2<\/sup>. (3)<\/li>\n
                          3. Is it equal to (A + B) (A – B)? Give reason (2)<\/li>\n<\/ol>\n

                            Answer:
                            \n1. 2A = A + B + A – B
                            \n\"Plus<\/p>\n

                            2.
                            \n\"Plus<\/p>\n

                            3. (A + B)(A – B)
                            \n\"Plus
                            \n(A + B)(A – B) = A2<\/sup> + AB – BA – B2<\/sup>
                            \n\u2260 A2<\/sup> – B2<\/sup>
                            \n\u2235 AB \u2260 BA.<\/p>\n

                            Question 11.
                            \n(i) Consider A = \\(\\left[\\begin{array}{lll}{1} & {x} & {1}\\end{array}\\right]\\), B = \\(\\left[\\begin{array}{ccc}{1} & {3} & {2} \\\\{2} & {5} & {1} \\\\{15} & {3} & {2}
                            \n\\end{array}\\right]\\), C = \\(\\left[\\begin{array}{l}{1} \\\\{2} \\\\{x}\\end{array}\\right]\\) (2)<\/p>\n\n\n\n\n\n\n\n\n
                            A – Matrix<\/td>\nB – Order<\/td>\n<\/tr>\n
                            A<\/td>\n3 \u00d7 1<\/td>\n<\/tr>\n
                            B<\/td>\n1 \u00d7 1<\/td>\n<\/tr>\n
                            BC<\/td>\n2 \u00d7 2<\/td>\n<\/tr>\n
                            ABC<\/td>\n3 \u00d7 3<\/td>\n<\/tr>\n
                            <\/td>\n1 \u00d7 3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            (ii) Find x if ABC = 0 (4)
                            \nAnswer:
                            \n(i)<\/p>\n\n\n\n\n\n\n\n
                            A – Matrix<\/td>\nB – Order<\/td>\n<\/tr>\n
                            A<\/td>\n1 \u00d7 3<\/td>\n<\/tr>\n
                            B<\/td>\n3 \u00d7 3<\/td>\n<\/tr>\n
                            BC<\/td>\n3 \u00d7 1<\/td>\n<\/tr>\n
                            ABC<\/td>\n1 \u00d7 1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            (ii) Given, ABC = 0
                            \n\"Plus
                            \n\u21d2 x2<\/sup> + 16x + 28 = 0
                            \n\u21d2 (x + 14)(x + 2) = 0
                            \n\u21d2 x = -14, -2.<\/p>\n

                            We hope the given Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices will help you. If you have any query regarding Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"

                            Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices are part of Plus Two Maths Chapter Wise Questions and Answers. Here we have given Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices. Board SCERT, Kerala Text Book NCERT Based Class Plus Two Subject Maths\u00a0Chapter Wise Questions Chapter Chapter 3 Chapter … Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[42728],"tags":[],"yoast_head":"\nPlus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices\" \/>\n<meta property=\"og:description\" content=\"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices are part of Plus Two Maths Chapter Wise Questions and Answers. Here we have given Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices. Board SCERT, Kerala Text Book NCERT Based Class Plus Two Subject Maths\u00a0Chapter Wise Questions Chapter Chapter 3 Chapter ... Read more\" \/>\n<meta property=\"og:url\" content=\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/\" \/>\n<meta property=\"og:site_name\" content=\"CBSE Library\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/aplustopper\/\" \/>\n<meta property=\"article:published_time\" content=\"2019-02-15T10:14:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-11-19T13:54:35+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/02\/Plus-Two-Maths-Chapter-Wise-Questions-and-Answers-Chapter-3-Matrices-3M-Q2.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Raju\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/cbselibrary.com\/#organization\",\"name\":\"Aplus Topper\",\"url\":\"https:\/\/cbselibrary.com\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/aplustopper\/\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"contentUrl\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"width\":1585,\"height\":375,\"caption\":\"Aplus Topper\"},\"image\":{\"@id\":\"https:\/\/cbselibrary.com\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/cbselibrary.com\/#website\",\"url\":\"https:\/\/cbselibrary.com\/\",\"name\":\"CBSE Library\",\"description\":\"Improve your Grades\",\"publisher\":{\"@id\":\"https:\/\/cbselibrary.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/cbselibrary.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/02\/Plus-Two-Maths-Chapter-Wise-Questions-and-Answers-Chapter-3-Matrices-3M-Q2.jpg\",\"contentUrl\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/02\/Plus-Two-Maths-Chapter-Wise-Questions-and-Answers-Chapter-3-Matrices-3M-Q2.jpg\",\"width\":374,\"height\":184,\"caption\":\"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices 3M Q2\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#webpage\",\"url\":\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/\",\"name\":\"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices - CBSE Library\",\"isPartOf\":{\"@id\":\"https:\/\/cbselibrary.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#primaryimage\"},\"datePublished\":\"2019-02-15T10:14:21+00:00\",\"dateModified\":\"2020-11-19T13:54:35+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/cbselibrary.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices\"}]},{\"@type\":\"Article\",\"@id\":\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#webpage\"},\"author\":{\"@id\":\"https:\/\/cbselibrary.com\/#\/schema\/person\/bd70dda77c8f886a86b7f2142f75d9c2\"},\"headline\":\"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices\",\"datePublished\":\"2019-02-15T10:14:21+00:00\",\"dateModified\":\"2020-11-19T13:54:35+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#webpage\"},\"wordCount\":1993,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/cbselibrary.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/02\/Plus-Two-Maths-Chapter-Wise-Questions-and-Answers-Chapter-3-Matrices-3M-Q2.jpg\",\"articleSection\":[\"HSSLiVE\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#respond\"]}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/cbselibrary.com\/#\/schema\/person\/bd70dda77c8f886a86b7f2142f75d9c2\",\"name\":\"Raju\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/38ccf4a5413b0ede9fc79802993d6981?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/38ccf4a5413b0ede9fc79802993d6981?s=96&d=mm&r=g\",\"caption\":\"Raju\"},\"url\":\"https:\/\/cbselibrary.com\/author\/raju\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices - CBSE Library","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/","og_locale":"en_US","og_type":"article","og_title":"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices","og_description":"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices are part of Plus Two Maths Chapter Wise Questions and Answers. Here we have given Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices. Board SCERT, Kerala Text Book NCERT Based Class Plus Two Subject Maths\u00a0Chapter Wise Questions Chapter Chapter 3 Chapter ... Read more","og_url":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/","og_site_name":"CBSE Library","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2019-02-15T10:14:21+00:00","article_modified_time":"2020-11-19T13:54:35+00:00","og_image":[{"url":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/02\/Plus-Two-Maths-Chapter-Wise-Questions-and-Answers-Chapter-3-Matrices-3M-Q2.jpg"}],"twitter_card":"summary","twitter_misc":{"Written by":"Raju","Est. reading time":"10 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/cbselibrary.com\/#organization","name":"Aplus Topper","url":"https:\/\/cbselibrary.com\/","sameAs":["https:\/\/www.facebook.com\/aplustopper\/"],"logo":{"@type":"ImageObject","@id":"https:\/\/cbselibrary.com\/#logo","inLanguage":"en-US","url":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","contentUrl":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","width":1585,"height":375,"caption":"Aplus Topper"},"image":{"@id":"https:\/\/cbselibrary.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/cbselibrary.com\/#website","url":"https:\/\/cbselibrary.com\/","name":"CBSE Library","description":"Improve your Grades","publisher":{"@id":"https:\/\/cbselibrary.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/cbselibrary.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#primaryimage","inLanguage":"en-US","url":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/02\/Plus-Two-Maths-Chapter-Wise-Questions-and-Answers-Chapter-3-Matrices-3M-Q2.jpg","contentUrl":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/02\/Plus-Two-Maths-Chapter-Wise-Questions-and-Answers-Chapter-3-Matrices-3M-Q2.jpg","width":374,"height":184,"caption":"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices 3M Q2"},{"@type":"WebPage","@id":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#webpage","url":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/","name":"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices - CBSE Library","isPartOf":{"@id":"https:\/\/cbselibrary.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#primaryimage"},"datePublished":"2019-02-15T10:14:21+00:00","dateModified":"2020-11-19T13:54:35+00:00","breadcrumb":{"@id":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/cbselibrary.com\/"},{"@type":"ListItem","position":2,"name":"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices"}]},{"@type":"Article","@id":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#article","isPartOf":{"@id":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#webpage"},"author":{"@id":"https:\/\/cbselibrary.com\/#\/schema\/person\/bd70dda77c8f886a86b7f2142f75d9c2"},"headline":"Plus Two Maths Chapter Wise Questions and Answers Chapter 3 Matrices","datePublished":"2019-02-15T10:14:21+00:00","dateModified":"2020-11-19T13:54:35+00:00","mainEntityOfPage":{"@id":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#webpage"},"wordCount":1993,"commentCount":0,"publisher":{"@id":"https:\/\/cbselibrary.com\/#organization"},"image":{"@id":"https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#primaryimage"},"thumbnailUrl":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2019\/02\/Plus-Two-Maths-Chapter-Wise-Questions-and-Answers-Chapter-3-Matrices-3M-Q2.jpg","articleSection":["HSSLiVE"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/cbselibrary.com\/plus-two-maths-chapter-wise-questions-answers-chapter-3\/#respond"]}]},{"@type":"Person","@id":"https:\/\/cbselibrary.com\/#\/schema\/person\/bd70dda77c8f886a86b7f2142f75d9c2","name":"Raju","image":{"@type":"ImageObject","@id":"https:\/\/cbselibrary.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/38ccf4a5413b0ede9fc79802993d6981?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/38ccf4a5413b0ede9fc79802993d6981?s=96&d=mm&r=g","caption":"Raju"},"url":"https:\/\/cbselibrary.com\/author\/raju\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/posts\/37832"}],"collection":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/comments?post=37832"}],"version-history":[{"count":0,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/posts\/37832\/revisions"}],"wp:attachment":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/media?parent=37832"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/categories?post=37832"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/tags?post=37832"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}