Ex 3.3 Class 12 NCERT Solutions Question 1.<\/strong> \nFind the transpose of each of the following matrices: \n(i) \\(\\left[ \\begin{matrix} 5 \\\\ \\frac { 1 }{ 2 } \\\\ -1 \\end{matrix} \\right] \\) \n(ii) \\(\\begin{bmatrix} 1 & -1 \\\\ 2 & 3 \\end{bmatrix}\\) \n(iii) \\(\\left[ \\begin{matrix} -1 & 5 & 6 \\\\ \\sqrt { 3 } & 5 & 6 \\\\ 2 & 3 & -1 \\end{matrix} \\right] \\) \nSolution: \n <\/p>\nQuestion 2. \nIf \\(A=\\left[ \\begin{matrix} -1 & 2 & 3 \\\\ 5 & 7 & 9 \\\\ -2 & 1 & 1 \\end{matrix} \\right] ,B=\\left[ \\begin{matrix} -4 & 1 & -5 \\\\ 1 & 2 & 0 \\\\ 1 & 3 & 1 \\end{matrix} \\right] \\) \nthen verify that: \n(i) (A + B)’ = A’ + B’ \n(ii) (A – B)’ = A’ – B’ \nSolution: \ni. (A + B) \n \nFrom (1) and (2), (A + B)’ = A’ + B’<\/p>\n
ii. (A – B) \n \nFrom (1) and (2), (A – B)’ = A’ – B’.<\/p>\n
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Question 3. \nIf \\(A’=\\left[ \\begin{matrix} 3 & 4 \\\\ -1 & 2 \\\\ 0 & 1 \\end{matrix} \\right] ,B=\\left[ \\begin{matrix} -1 & 2 & 1 \\\\ 1 & 2 & 3 \\end{matrix} \\right] \\) \nthen verify that: \n(i) (A+B)’ = A’+B’ \n(ii) (A-B)’ = A’-B’ \nSolution: \n <\/p>\n
Question 4. \nIf \\(A’=\\begin{bmatrix} -2 & 3 \\\\ 1 & 2 \\end{bmatrix} ,B=\\begin{bmatrix} -1 & 0 \\\\ 1 & 2 \\end{bmatrix} \\) then find (A+2B)’ \nSolution: \n <\/p>\n
Question 5. \nFor the matrices A and B, verify that (AB)’ = B’A’, where \n\\((i)\\quad A=\\left[ \\begin{matrix} 1 \\\\ -4 \\\\ 3 \\end{matrix} \\right] ,B=\\left[ \\begin{matrix} -1 & 2 & 1 \\end{matrix} \\right] \\) \n\\((ii)\\quad A=\\left[ \\begin{matrix} 0 \\\\ 1 \\\\ 2 \\end{matrix} \\right] ,B=\\left[ \\begin{matrix} 1 & 5 & 7 \\end{matrix} \\right] \\) \nSolution: \n\\((i)\\quad A=\\left[ \\begin{matrix} 1 \\\\ -4 \\\\ 3 \\end{matrix} \\right] \\) \n\\(A’=\\left[ \\begin{matrix} 1 & -4 & 3 \\end{matrix} \\right] \\) \n <\/p>\n
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Question 6. \nIf (i) \\(A=\\begin{bmatrix} cos\\alpha & \\quad sin\\alpha \\\\ -sin\\alpha & \\quad cos\\alpha \\end{bmatrix} \\) , the verify that A’A = I \nIf (ii) \\(A=\\begin{bmatrix} sin\\alpha & \\quad cos\\alpha \\\\ -cos\\alpha & \\quad sin\\alpha \\end{bmatrix} \\), the verify that A’A = I \nSolution: \n <\/p>\n
Question 7. \n(i) Show that the matrix \\(A=\\left[ \\begin{matrix} 1 & -1 & 5 \\\\ -1 & 2 & 1 \\\\ 5 & 1 & 3 \\end{matrix} \\right] \\) is a symmetric matrix. \n(ii) Show that the matrix \\(A=\\left[ \\begin{matrix} 0 & 1 & -1 \\\\ -1 & 0 & 1 \\\\ 1 & -1 & 0 \\end{matrix} \\right] \\) is a skew-symmetric matrix. \nSolution: \n(i) \\(A=\\left[ \\begin{matrix} 1 & -1 & 5 \\\\ -1 & 2 & 1 \\\\ 5 & 1 & 3 \\end{matrix} \\right] \\), A’ = \\(\\left[ \\begin{matrix} 1 & -1 & 5 \\\\ -1 & 2 & 1 \\\\ 5 & 1 & 3 \\end{matrix} \\right] \\) = A \nA is symmetric matrix, since A’ = A<\/p>\n
(ii) \\(A=\\begin{bmatrix} sin\\alpha & \\quad cos\\alpha \\\\ -cos\\alpha & \\quad sin\\alpha \\end{bmatrix} \\) \nA’ = \\(\\left[ \\begin{matrix} 0 & 1 & -1 \\\\ -1 & 0 & 1 \\\\ 1 & -1 & 0 \\end{matrix} \\right] \\) = – 1\\(\\left[ \\begin{matrix} 0 & 1 & -1 \\\\ -1 & 0 & 1 \\\\ 1 & -1 & 0 \\end{matrix} \\right] \\) \nA’ = – A \nA is a skew-symmetric matrix, since A’ = A<\/p>\n
Question 8. \nFor the matrix, \\(A=\\begin{bmatrix} 1 & 5 \\\\ 6 & 7 \\end{bmatrix}\\) \n(i) (A + A’) is a symmetric matrix. \n(ii) (A – A’) is a skew-symmetric matrix. \nSolution: \n <\/p>\n
Question 9. \nFind \\(\\\\ \\frac { 1 }{ 2 } (A+A’)\\) and \\(\\\\ \\frac { 1 }{ 2 } (A-A’)\\), when \\(A=\\left[ \\begin{matrix} 0 & a & b \\\\ -a & 0 & c \\\\ -b & -c & 0 \\end{matrix} \\right] \\) \nSolution: \n <\/p>\n
<\/p>\n
Question 10. \nExpress the following matrices as the sum of a symmetric and a skew-symmetric matrix. \n(i) \\(\\begin{bmatrix} 3 & 5 \\\\ 1 & -1 \\end{bmatrix}\\) \n(ii) \\(\\left[ \\begin{matrix} 6 & -2 & 2 \\\\ -2 & 3 & -1 \\\\ 2 & -1 & 3 \\end{matrix} \\right] \\) \n(iii) \\(\\left[ \\begin{matrix} 3 & 3 & -1 \\\\ -2 & -2 & 1 \\\\ -4 & -5 & 2 \\end{matrix} \\right] \\) \n(iv) \\(\\begin{bmatrix} 1 & 5 \\\\ -1 & 2 \\end{bmatrix}\\) \nSolution: \n \nThus A can be represented as a sum of a symmetric and a skew-symmetric matrix.<\/p>\n
\nThus B can be expressed as the sum of a symmetric and a skew-symmetric matrix.<\/p>\n
\nThus A can be expressed as the sum of a symmetric and skew-symmetric matrix.<\/p>\n
\nThus D can be expressed as the sum of a symmetric and a skew-symmetric matrix.<\/p>\n
<\/p>\n
Question 11. \nChoose the correct answer in the following questions: \nIf A, B are symmetric matrices of same order then AB-BA is a \n(a) Skew – symmetric matrix \n(b) Symmetric matrix \n(c) Zero matrix \n(d) Identity matrix \nSolution: \nNow A’ = B, B’ = B \n(AB – BA)’ = (AB)’ – (BA)\u2019 \n= B’A’ – A’B’ \n= BA – AB \n= – (AB – BA) \nAB – BA is a skew-symmetric matrix Hence, option (a) is correct.<\/p>\n
Question 12. \nIf \\(A=\\begin{bmatrix} cos\\alpha & \\quad -sin\\alpha \\\\ sin\\alpha & \\quad cos\\alpha \\end{bmatrix}\\) then A+A’ = I, if the \nvalue of \u03b1 is \n(a) \\(\\frac { \\pi }{ 6 } \\) \n(b) \\(\\frac { \\pi }{ 3 } \\) \n(c) \u03c0 \n(d) \\(\\frac { 3\\pi }{ 2 } \\) \nSolution: \nNow \n \nThus option (b) is correct.<\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-3-ex-3-3\/ NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.3 Ex 3.3 Class 12 NCERT Solutions Question 1. Find the transpose of each of the following matrices: (i) (ii) (iii) …<\/p>\n
NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3<\/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 3.3 - 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