NCERT Solutions for Class 12 Maths<\/a> Chapter 3 Matrices Ex 3.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-3-ex-3-1\/<\/p>\nNCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.1<\/h2>\n <\/p>\n
Ex 3.1 Class 12 NCERT Question 1.<\/strong> \nIn the matrix A = \\(\\left[\\begin{array}{cccc} 2 & 5 & 19 & -7 \\\\ 35 & -2 & \\frac{5}{2} & 12 \\\\ \\sqrt{3} & 1 & -5 & 17 \\end{array}\\right]\\), write \ni. the order of the matrix, \nii. the number of elements. \niii. Write the elements a13<\/sub>, a21<\/sub>, a33<\/sub>, a24<\/sub>, a23<\/sub>. \nSolution: \ni. The matrix has 3 rows and 4 columns. Hence the order of A is 3 x 4<\/p>\nii. Number of elements = 3(4) = 12<\/p>\n
iii. a13<\/sub> = 19, \na21<\/sub> = 35, \na33<\/sub> = – 5, \na24<\/sub> = 12, \na23<\/sub> = \\(\\frac { 5 }{ 2 }\\)<\/p>\nClass 12 Maths Ex 3.1 NCERT Question 2.<\/strong> \nIf a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements? \nSolution: \nThe ordered pairs of natural numbers whose product is 24 are (1, 24), (2, 12), (3, 8), (4, 6), (6,4), (8,3), (12,2) and (24,1). Hence the possible orders are 1 X 24, 2 x 12, 3 x 3, 8, 4 x 6, 6 x 4, 8 x 3, 12 x 2, 24 x 1. \nThe possible orders with 13 elements are 1 x 13, 13 x 1<\/p>\n <\/p>\n
Exercise 3.1 Class 12 Maths NCERT\u00a0 Question 3.<\/strong> \nIf a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements? \nSolution: \nThe ordered pairs of natural numbers whose product is 18 are (1, 18), (2, 9), (3, 6), (6, 3), (9, 2) and (18, 1). \nHence the possible orders are 1 x 18, 2 x 9, 3 x 6, 6 x 3, 9 x 2, 1.8 x 1 \nThe possible orders with 5 elements are 1 x 5, 5 x 1.<\/p>\nClass 12 Chapter 3 Exercise 3.1 NCERT Question 4.<\/strong> \nConstruct a 2 x 2 matrix, A = [aij<\/sub>], whose elements are given by \ni. aij<\/sub> = \\(\\frac{(i+j)^{2}}{2}\\) \nii. aij<\/sub> = \\(\\frac{i}{j}\\) \niii. aij<\/sub> = \\(\\frac{(i+2j)^{2}}{2}\\) \nSolution: \n <\/p>\n <\/p>\n
Question 5. \nConstruct a 3 x 4 matrix, whose elements are given by \ni. aij<\/sub> = \\(\\frac{1}{2}\\)|-3i + j| \ni. aij<\/sub> = 2i – j \nSolution: \nThe general form of a 3 x 4 matrix is \n <\/p>\nii. The general form of a 3 x 4 matrix is \n <\/p>\n
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Question 6. \nFind the values of x, y and z from the following equations: \ni. \\(\\left[\\begin{array}{ll} \n4 & 3 \\\\ \nx & 5 \n\\end{array}\\right]=\\left[\\begin{array}{ll} \ny & z \\\\ \n1 & 5 \n\\end{array}\\right]\\) \nii. \\(\\left[\\begin{array}{cc} \nx+y & 2 \\\\ \n5+z & x y \n\\end{array}\\right]=\\left[\\begin{array}{cc} \n6 & 2 \\\\ \n5 & 8 \n\\end{array}\\right]\\) \niii. \\(\\left[\\begin{array}{c} \nx+y+z \\\\ \nx+z \\\\ \ny+z \n\\end{array}\\right]=\\left[\\begin{array}{l} \n9 \\\\ \n5 \\\\ \n7 \n\\end{array}\\right]\\) \nSolution: \ni. \\(\\left[\\begin{array}{ll} \n4 & 3 \\\\ \nx & 5 \n\\end{array}\\right]=\\left[\\begin{array}{ll} \ny & z \\\\ \n1 & 5 \n\\end{array}\\right]\\) \nComparing the corresponding elements of the two matrices, we get x = 1, y = 4, z = 3.<\/p>\n
ii. \\(\\left[\\begin{array}{cc} \nx+y & 2 \\\\ \n5+z & x y \n\\end{array}\\right]=\\left[\\begin{array}{cc} \n6 & 2 \\\\ \n5 & 8 \n\\end{array}\\right]\\) \nEquating the corresponding elements, we get \nx + y = 6, 5 + z = 5, xy = 8 \nSolving we get x = 2, y = 4, z = 0 \nor x = 4, y = 2, z = 0<\/p>\n
iii. \\(\\left[\\begin{array}{c} \nx+y+z \\\\ \nx+z \\\\ \ny+z \n\\end{array}\\right]=\\left[\\begin{array}{l} \n9 \\\\ \n5 \\\\ \n7 \n\\end{array}\\right]\\) \n\u21d2 x + y + z = 9 … (1) \nx + z = 5 … (2) \ny + z = 7 … (3) \n(2) + (3) \u21d2 x + y + 2z = 12 \n(1) \u21d2 x + y + z = 9 \nSubtracting we get z = 3 \n\u2234 x = 2,y = 4, z = 3<\/p>\n
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Question 7. \nFind the value of a, b, c and d from the equation: \n\\(\\left[\\begin{array}{cc} \na-b & 2 a+c \\\\ \n2 a-b & 3 c+d \n\\end{array}\\right]=\\left[\\begin{array}{cc} \n-1 & 5 \\\\ \n0 & 13 \n\\end{array}\\right]\\) \nSolution: \n\\(\\left[\\begin{array}{cc} \na-b & 2 a+c \\\\ \n2 a-b & 3 c+d \n\\end{array}\\right]=\\left[\\begin{array}{cc} \n-1 & 5 \\\\ \n0 & 13 \n\\end{array}\\right]\\) \nEquating the corresponding elements of the two matrices, we get \na – b = – 1 ………… (1) \n2a + c = 5 ……….. (2) \n2a – b = 0 ……….. (3) \n3c + d = 13 ……….. (4) \n(3) – (1) \u21d2 a = 1 \n(3) \u21d2 b = 2 \n(2) \u21d2 c = 3 \n(4) \u21d2 d = 4<\/p>\n
Question 8. \nA = [a]m x n<\/sub> is a square matrix, if \n(a) m n \n(c) m = n \n(d) None of these \nSolution: \n(c) m = n \nFor a square matrix \nNumber of rows = Number of columns \n\u2234 m = n<\/p>\n <\/p>\n
Question 9. \nWhich of the given values of x and y make the following pair of matrices equal? \n\\(\\left[\\begin{array}{cc} \n3 x+7 & 5 \\\\ \ny+1 & 2-3 x \n\\end{array}\\right],\\left[\\begin{array}{cc} \n0 & y-2 \\\\ \n8 & 4 \n\\end{array}\\right]\\) \n(a) x= \\(\\frac { -1 }{ 3 }\\), y = 7 \n(b) Not possible to find \n(c) y = 7, x = \\(\\frac { -2 }{ 3 }\\) \n(d) x = \\(\\frac { -1 }{ 3 }\\), y = \\(\\frac { – 2 }{ 3 }\\) \nSolution: \n(b) For equal matrices, the corresponding elements are equal. Equating the corre-spondingelements, we get x = \\(\\frac { -7 }{ 3 }\\), y = 7, y = 7 and x = \\(\\frac { -2 }{ 3 }\\) \nx has 2 values which is not possible.<\/p>\n
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Question 10. \nThe number of all possible matrices of order 3 x 3 with each entry 0 or 1 is: \n(a) 27 \n(b) 18 \n(c) 81 \n(d) 512 \nSolution: \n(d) 512 \nThere are 9 elements and each element can be either 0 or 1. \nThe 9 places can be filled in 29 ways. \n\u2234 Total number of ways = 29 = 512<\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-3-ex-3-1\/ NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.1 Ex 3.1 Class 12 NCERT Question 1. In the matrix A = , write i. the order of the matrix, …<\/p>\n
NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.1<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.1 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n