{"id":29302,"date":"2023-10-31T15:06:48","date_gmt":"2023-10-31T09:36:48","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=29302"},"modified":"2023-11-01T11:49:39","modified_gmt":"2023-11-01T06:19:39","slug":"ncert-solutions-for-class-12-maths-chapter-3-ex-3-1","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-12-maths-chapter-3-ex-3-1\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.1"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 3 Matrices Ex 3.1 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.1<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\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>\n

ii. 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>\n

Question 2.
\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

\"NCERT<\/p>\n

Question 3.
\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>\n

Question 4.
\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\"NCERT<\/p>\n

\"NCERT<\/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\"NCERT<\/p>\n

ii. The general form of a 3 x 4 matrix is
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

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

\"NCERT<\/p>\n

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

\"NCERT<\/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

\"NCERT<\/p>\n

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. NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.1 Question 1. In the matrix A = , write i. the order of the matrix, ii. the number of elements. iii. …<\/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":{"spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.1 - NCERT Solutions<\/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:\/\/ncertsolutions.guru\/ncert-solutions-for-class-12-maths-chapter-3-ex-3-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.1 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.1 Questions and Answers are prepared by our highly skilled subject experts. 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NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.1 Question 1. 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