{"id":39854,"date":"2023-01-19T10:00:55","date_gmt":"2023-01-19T04:30:55","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=39854"},"modified":"2023-01-20T09:40:15","modified_gmt":"2023-01-20T04:10:15","slug":"plus-two-maths-chapter-wise-previous-questions-chapter-3","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-chapter-3\/","title":{"rendered":"Plus Two Maths Chapter Wise Previous Questions Chapter 3 Matrices"},"content":{"rendered":"

Plus Two Maths Chapter Wise Previous Questions Chapter 3 Matrices are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers<\/a>. Here we have given Plus Two Maths Chapter Wise Previous Chapter 3 Matrices.<\/p>\n

Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 3 Matrices<\/h2>\n

Plus Two Maths Matrices 3 Marks Important Questions<\/h3>\n

Question 1.
\nWrite A as the sum of a symmetric and a skew-symmetric matrix. \\(A=\\left[\\begin{array}{ccc}
\n1 & 4 & -1 \\\\
\n2 & 5 & 4 \\\\
\n-1 & -6 & 3
\n\\end{array}\\right]\\)\u00a0(March – 2010)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 2.
\nConsider the matrices
\n\\(A=\\left[\\begin{array}{lll}
\n2 & 1 & 3 \\\\
\n2 & 3 & 1 \\\\
\n1 & 1 & 1
\n\\end{array}\\right] \\text { and } B=\\left[\\begin{array}{ccc}
\n-1 & 2 & 3 \\\\
\n-2 & 3 & 1 \\\\
\n-1 & 1 & 1
\n\\end{array}\\right]\\)
\n(i) Find A+B
\n(ii) Find (A + B) (A-B) (May -2010)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 3.
\nGiven \\(P=\\left[\\begin{array}{cc}
\n2 & -3 \\\\
\n-1 & 2
\n\\end{array}\\right]\\) Find the inverse of P by elementary row operation. (March 2011)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 4.
\nLet \\(A=\\left[\\begin{array}{lll}
\n3 & 6 & 5 \\\\
\n6 & 7 & 8
\n\\end{array}\\right] \\text { and } C=\\left[\\begin{array}{ccc}
\n1 & 2 & -3 \\\\
\n4 & 5 & 6
\n\\end{array}\\right]\\)<\/p>\n

(i) Find 2A
\n(ii) Find the matrix B such that 2A + B = 3C (May 2011)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 5.
\nLet \\(A=\\left[\\begin{array}{cc}
\n2 & 4 \\\\
\n-1 & 1
\n\\end{array}\\right]\\)
\n(i) Apply elementary transformation R \u2192 R R1\/2 in the matrix A.
\n(ii) Find the inverse of A by the elementary transformation. (May 2011)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 6.
\nConsider the matrix \\(A=\\left[\\begin{array}{cc}
\n3 & 1 \\\\
\n-1 & 2
\n\\end{array}\\right]\\)
\n(i) Find A2<\/sup>
\n(ii) Find ksothat A2 = kA – 7I (March – 2012)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 7.
\nConsider a 2×2 matrix
\n\\(A=\\left[a_{i j}\\right]$ where $a_{i j}=|2 i-3 j|\\)
\n(i) Write A
\n(ii) Find A + AT<\/sup> (March – 2012)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 8.
\nIf \\(A=\\left[\\begin{array}{cc}
\n3 & 1 \\\\
\n-1 & 2
\n\\end{array}\\right]\\) then
\n(i) Find A2<\/sup>
\n(ii) Hence show that A2<\/sup>\u00a0– 5A + 7I = 0. (March 2013)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 9.
\nIf a matrix \\(A=\\left[\\begin{array}{ll}3 x & x \\\\ -x & 2 x\\end{array}\\right]\\) is a solution of the equation x2<\/sup> – 5x + 7 = 0, find any one value of X. (May 2013)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 10.
\nConsider the matrices \\(A=\\left[\\begin{array}{cc}1 & -2 \\\\ -1 & 3\\end{array}\\right]$ and $B=\\left[\\begin{array}{ll}a & b \\\\ c & d\\end{array}\\right]$\\) \\(A B=\\left[\\begin{array}{ll}2 & 9 \\\\ 5 & 6\\end{array}\\right]\\), find the values of a,b,c,d (March – 2014)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 11.
\nConsider a 2 x 2 matrix A=[aij<\/sub>] Where \\(a_{i j}=\\frac{(i+2 j)^{2}}{2}\\)
\n(i) Write A
\n(ii) Find A + AT<\/sup> (March – 2014)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 12.
\nIf X + Y = \\(\\left[\\begin{array}{ll}7 & 0 \\\\ 2 & 5\\end{array}\\right]\\) and X – Y = \\(\\left[\\begin{array}{ll}3 & 0 \\\\ 0 & 3\\end{array}\\right]\\) then
\n(i) Find X and Y.
\n(ii) Find 2X + Y. (May – 2014)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 13.
\ni) If A, B are symmetric matrices of same order then AB – BA is always a ………….
\nA) Skew-Symmetric matrix
\nB) Symmetric matrix
\nC) Identity matrix
\nD) Zero matrix
\n(ii) For the matrix \\(A=\\left[\\begin{array}{ll}2 & 4 \\\\ 5 & 6\\end{array}\\right]\\), verify that A + AT<\/sup> is a symmetric matrix. (March – 2015)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 14.
\nConsider the matrix \\(A=\\left[\\begin{array}{ll}3 & -2 \\\\ 4 & -2\\end{array}\\right]\\)
\n(i) Find A2<\/sup>
\n(ii) Find k so that A2<\/sup> = kA – 21 (May – 2015)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Plus Two Maths Matrices 4 Marks Important Questions<\/h3>\n

Question 1.
\n(i) Find the value of x and y from the equations \\(a\\left[\\begin{array}{cc}x & 5 \\\\ 7 & y-3\\end{array}\\right]+\\left[\\begin{array}{cc}3 & -4 \\\\ 1 & 2\\end{array}\\right]=\\left[\\begin{array}{cc}7 & 6 \\\\ 15 & 14\\end{array}\\right]\\)
\n(ii) Given \\(A=\\left[\\begin{array}{cc}1 & 2 \\\\ 3 & -1 \\\\ 4 & 2\\end{array}\\right], B=\\left[\\begin{array}{ccc}-1 & 4 & -5 \\\\ 2 & 1 & 0\\end{array}\\right]\\) Show that AB \u2260 BA (March – 2011)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 2.
\n(i) Find a, b matrix \\(\\left[\\begin{array}{ccc}0 & 3 & a \\\\ b & 0 & -2 \\\\ 5 & 2 & 0\\end{array}\\right]\\) is skew symmetric matrix.
\n(ii) Express \\(A=\\left[\\begin{array}{ccc}7 & 3 & -5 \\\\ 0 & 1 & 5 \\\\ -2 & 7 & 3\\end{array}\\right]\\) sum of a symmetric and a skew symmetric matrix. (May – 2012)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 3.
\nConsider the matrices \\(A=\\left[\\begin{array}{cc}2 & -6 \\\\ 1 & 2\\end{array}\\right]$ and $A+3 B=\\left[\\begin{array}{cc}5 & -3 \\\\ -2 & -1\\end{array}\\right]\\)
\n(i) Find matrix B
\n(il) Find matrix AB.
\n(iii) Find the transpose of B. (May – 2013)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 4.
\n(i) The value of k such that matrix \\(\\left[\\begin{array}{cc} 1 & k \\\\ -k & 1 \\end{array}\\right]\\) is symmetric if
\n(a) 0
\n(b) 1
\n(c) – 1
\n(d) 2<\/p>\n

(ii) If \\(A=\\left[\\begin{array}{cc}
\n\\cos \\theta & \\sin \\theta \\\\
\n-\\sin \\theta & \\cos \\theta
\n\\end{array}\\right]\\) then prove that \\(A^{2}=\\left[\\begin{array}{cc}
\n\\cos 2 \\theta & \\sin 2 \\theta \\\\
\n-\\sin 2 \\theta & \\cos 2 \\theta
\n\\end{array}\\right]\\)
\n\\(\\text { (iii) if } A=\\left[\\begin{array}{ll}
\n1 & 3 \\\\
\n4 & 1
\n\\end{array}\\right], \\text { then find }\\left|3 A^{T}\\right|\\) (March – 2017)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Plus Two Maths Matrices 6 Marks Important Questions<\/h3>\n

Question 1.
\nLet A be a matrix of order 3 x 3 whose elements are given by aij<\/sub>\u00a0= 21 – j
\n(i) Obtain the matrix A.
\n(ii) Find AT Also express A as the sum of symmetric and skew-symmetric matrix.\u00a0(March – 2010)<\/span>
\nAnswer:
\n\"Plus<\/p>\n

Question 2.
\nConsider a 2 x 2 matrix \\(A=\\left[a_{\\theta}\\right]\\) with aij<\/sub> = 2i<\/sup> + j
\n(i) Construct A.
\n(ii) Find A + AT<\/sup>, A – AT<\/sup>
\n(iii) Express A as sum of a symmetric and skew-symmetric matrix.\u00a0(May -2015)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 3.
\n(i) \\(A=\\left[\\begin{array}{ll}
\n0 & 1 \\\\
\n0 & 0
\n\\end{array}\\right], B=\\left[\\begin{array}{ll}
\n1 & 0 \\\\
\n0 & 0
\n\\end{array}\\right]\\) then BA = _____
\n\\(\\begin{array}{l}
\n\\text { (a) }\\left[\\begin{array}{ll}
\n1 & 0 \\\\
\n0 & 1
\n\\end{array}\\right] & \\text { (b) }\\left[\\begin{array}{ll}
\n0 & 1 \\\\
\n1 & 0
\n\\end{array}\\right] \\\\
\n\\text { (c) }\\left[\\begin{array}{ll}
\n0 & 1 \\\\
\n0 & 0
\n\\end{array}\\right] & \\text { (d) }\\left[\\begin{array}{ll}
\n0 & 0 \\\\
\n0 & 0
\n\\end{array}\\right]
\n\\end{array}\\)<\/p>\n

(ii) Write \\(A=\\left[\\begin{array}{cc}
\n3 & 5 \\\\
\n1 & -1
\n\\end{array}\\right]\\) as the sum of a symmetric and a skew symmetric matrix.
\n(iii) Find the inverse of \\(A=\\left[\\begin{array}{ll}
\n2 & -6 \\\\
\n1 & -2
\n\\end{array}\\right]\\) (March 2016)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 4.
\n(i) If the matrix A is both symmetric and skew-symmetric, then A is a
\n(a) diagonal matrix
\n(b) zero matrix
\n(c) square matrix
\n(d) scalar matrix<\/p>\n

(ii) If \\(A=\\left[\\begin{array}{cc}
\n1 & 3 \\\\
\n-2 & 4
\n\\end{array}\\right]\\), then show that<\/p>\n

(iii) Hence find A-1<\/sup> (May 2016)<\/span>
\nAnswer:
\n\"Plus
\n\"Plus<\/p>\n

Question 5.
\n(i) The number of all possible 2 x 2 matrices with entries O or 1 is
\n(a) 8
\n(b) 9
\n(c) 16
\n(d) 25<\/p>\n

(ii) If the area of a triangle whose vertices are (k,0), (5,0), (0,1) is 10 square units the find k.
\n(iii) Using elementary transformations find the inverse of the matrix \\(\\left[\\begin{array}{ll}
\n2 & 1 \\\\
\n1 & 1
\n\\end{array}\\right]\\) (May 2017)
\n<\/span>Answer:
\n\"Plus
\n\"Plus<\/p>\n

We hope the Plus Two Maths Chapter Wise Previous Questions Chapter 3 Matrices help you. If you have any query regarding Kerala Plus Two Maths Chapter Wise Previous Questions 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 Previous Questions Chapter 3 Matrices are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 3 Matrices. Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 3 Matrices Plus Two Maths Matrices 3 Marks Important Questions Question 1. Write […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[42728],"tags":[],"yoast_head":"\nPlus Two Maths Chapter Wise Previous Questions Chapter 3 Matrices - A Plus Topper<\/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:\/\/www.aplustopper.com\/plus-two-maths-chapter-wise-previous-questions-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 Previous Questions Chapter 3 Matrices\" \/>\n<meta property=\"og:description\" content=\"Plus Two Maths Chapter Wise Previous Questions Chapter 3 Matrices are part of\u00a0Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 3 Matrices. Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 3 Matrices Plus Two Maths Matrices 3 Marks Important Questions Question 1. 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Here we have given Plus Two Maths Chapter Wise Previous Chapter 3 Matrices. Kerala\u00a0Plus Two Maths Chapter Wise Previous\u00a0Questions Chapter 3 Matrices Plus Two Maths Matrices 3 Marks Important Questions Question 1. 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