{"id":29783,"date":"2022-03-29T11:00:15","date_gmt":"2022-03-29T05:30:15","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=29783"},"modified":"2022-03-29T11:22:24","modified_gmt":"2022-03-29T05:52:24","slug":"ncert-solutions-for-class-12-maths-chapter-4-ex-4-5","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-5\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.5"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 4 Determinants Ex 4.5 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-5\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.5<\/h2>\n

\"NCERT<\/p>\n

Ex 4.5 Class 12 NCERT Solutions Question 1.<\/strong>
\n\\(\\left[\\begin{array}{ll}
\n1 & 2 \\\\
\n3 & 4
\n\\end{array}\\right]\\)
\nSolution:
\nLet A = \\(\\left[\\begin{array}{ll}
\n1 & 2 \\\\
\n3 & 4
\n\\end{array}\\right]\\)
\nAdj A = \\(\\begin{bmatrix} 4 & -3 \\\\ -2 & 1 \\end{bmatrix}\\)<\/p>\n

Exercise 4.5 Class 12 NCERT Solutions Question 2.<\/strong>
\n\\(\\left[ \\begin{matrix} 1 & -1 & 2 \\\\ 2 & 3 & 5 \\\\ -2 & 0 & 1 \\end{matrix} \\right]\\)
\nSolution:
\n\"Exercise<\/p>\n

Exercise 4.5 Class 12 Maths Question 3.<\/strong>
\n\\(\\begin{bmatrix} 2 & 3 \\\\ -4 & 6 \\end{bmatrix}\\)
\nSolution:
\n\"Ex<\/p>\n

\"NCERT<\/p>\n

4.5 Class 12 NCERT Solutions Question 4.<\/strong>
\n\\(\\left[ \\begin{matrix} 1 & -1 & 2 \\\\ 3 & 0 & -2 \\\\ 1 & 0 & 3 \\end{matrix} \\right]\\)
\nSolution:
\n|A| = \\(\\left|\\begin{array}{ccc}
\n1 & -1 & 2 \\\\
\n3 & 0 & -2 \\\\
\n1 & 0 & 3
\n\\end{array}\\right|\\)
\nA11<\/sub> = 0, A12\u00a0<\/sub>= – 11, A13\u00a0<\/sub>= 0,
\nA21\u00a0<\/sub>= – 3, A22\u00a0<\/sub>= 1, A23\u00a0<\/sub>= 1,
\nA31<\/sub> = – 2, A32\u00a0<\/sub>= 8, A33\u00a0<\/sub>= 3
\n\"Class<\/p>\n

Ex 4.5 Class 12 Maths Ncert Solutions Question 5.<\/strong>
\n\\(\\begin{bmatrix} 2 & -2 \\\\ 4 & 3 \\end{bmatrix}\\)
\nSolution:
\n\"Class<\/p>\n

Exercise 4.5 Maths Class 12 Question 6.<\/strong>
\n\\(\\begin{bmatrix} -1 & 5 \\\\ -3 & 2 \\end{bmatrix}\\)
\nSolution:
\n\"Ex.4.5<\/p>\n

Exercise 4.5 Class 12 Maths Solutions Question 7.<\/strong>
\n\\(\\left[ \\begin{matrix} 1 & 2 & 3 \\\\ 0 & 2 & 4 \\\\ 0 & 0 & 5 \\end{matrix} \\right]\\)
\nSolution:
\n\"Solution<\/p>\n

\"NCERT<\/p>\n

Class 12 Maths Ch 4 Ex 4.5 Question 8.<\/strong>
\n\\(\\left[ \\begin{matrix} 1 & 0 & 0 \\\\ 3 & 3 & 0 \\\\ 5 & 2 & -1 \\end{matrix} \\right]\\)
\nSolution:
\n\"Ex<\/p>\n

Ex4.5 Class 12 NCERT Solutions Question 9.<\/strong>
\n\\(\\left[ \\begin{matrix} 2 & 1 & 3 \\\\ 4 & -1 & 0 \\\\ -7 & 2 & 1 \\end{matrix} \\right]\\)
\nSolution:
\n\"Exercise<\/p>\n

Ex 4.5 Class 12 Maths NCERT Solutions Question 10.<\/strong>
\n\\(\\left[ \\begin{matrix} 1 & -1 & 2 \\\\ 0 & 2 & -3 \\\\ 3 & -2 & 4 \\end{matrix} \\right]\\)
\nSolution:
\n\"Exercise<\/p>\n

\"NCERT<\/p>\n

Class 12 Maths Chapter 4 Exercise 4.5 Solutions Question 11.<\/strong>
\n\\(\\left[ \\begin{matrix} 1 & 0 & 0 \\\\ 0 & cos\\alpha & sin\\alpha \\\\ 0 & sin\\alpha & -cos\\alpha \\end{matrix} \\right] \\)
\nSolution:
\n\"4.5<\/p>\n

Ncert Solutions For Class 12 Maths Chapter 4 Exercise 4.5 Question 12.<\/strong>
\nLet \\(A=\\begin{bmatrix} 3 & 7 \\\\ 2 & 5 \\end{bmatrix},B=\\begin{bmatrix} 6 & 8 \\\\ 7 & 9 \\end{bmatrix}\\), verify that (AB)-1<\/sup> = B-1<\/sup>A-1<\/sup>
\nSolution:
\n\"Ex<\/p>\n

Class 12 Maths Chapter 4 Exercise 4.5 Question 13.<\/strong>
\nIf \\(A=\\begin{bmatrix} 3 & 1 \\\\ -1 & 2 \\end{bmatrix} \\) show that A\u00b2 – 5A + 7I = 0, hence find A-1<\/sup>.
\nSolution:
\n\"Exercise<\/p>\n

\"NCERT<\/p>\n

Class 12 Maths Chapter 4 Exercise 4.5 Solution Question 14.<\/strong>
\nFor the matrix A = \\(\\begin{bmatrix} 3 & 2 \\\\ 1 & 1 \\end{bmatrix} \\) find file numbers a and b such that A\u00b2 + aA + bI\u00b2 = 0. Hence, find A-1<\/sup>.
\nSolution:
\n\"Exercise<\/p>\n

Class 12 Maths Ex 4.5 Solutions Question 15.<\/strong>
\nFor the matrix \\(A=\\left[ \\begin{matrix} 1 & 1 & 1 \\\\ 1 & 2 & -3 \\\\ 2 & -1 & 3 \\end{matrix} \\right] \\)\u00a0Show that A\u00b3 – 6A\u00b2 + 5A + 11I3<\/sub>=0. Hence find A-1<\/sup>
\nSolution:
\n\"Class
\ni.e., A\u00b3 – 6A\u00b2 + 5A + 11I3<\/sub> = 0 … (1)
\n|A| = \\(\\left|\\begin{array}{ccc}
\n1 & 1 & 1 \\\\
\n1 & 2 & -3 \\\\
\n2 & -1 & 3
\n\\end{array}\\right|\\)
\n= 1(3) – 1(9) + 1(- 5) = – 11 \u2260 0
\n\u2234 A-1<\/sup> exists
\n\u21d2 (1) = A.A.A – 6A.A. + 5A = – 11 I
\n\u21d2 AA(AA-1<\/sup> – 6A(AA-1<\/sup>) + 5AA-1<\/sup> = – 11 IA-1<\/sup> (Multiplying by A-1<\/sup>)
\n\u21d2 A\u00b2I – 6AI + 5I = – 11A-1<\/sup>
\n\u21d2 A\u00b2 – 6A + 5I = – 11A-1<\/sup>
\n\u21d2 A-1<\/sup> = \\(\\frac { -1 }{ 11 }\\)[A\u00b2 – 6A + 5I]
\n\"Ex4.5<\/p>\n

\"NCERT<\/p>\n

Class 12 Ex 4.5 NCERT Solutions Question 16.<\/strong>
\nIf \\(A=\\left[ \\begin{matrix} 2 & -1 & 1 \\\\ -1 & 2 & -1 \\\\ 1 & -1 & 2 \\end{matrix} \\right] \\) show that A\u00b3 – 6A\u00b2 + 9A – 4I = 0 and hence, find A-1<\/sup>
\nSolution:
\n\"Ex<\/p>\n

Exercise 4.5 Class 12 Maths Ncert Solutions Question 17.<\/strong>
\nLet A be a non-singular square matrix of order 3 x 3. Then | Adj A | is equal to:
\n(a) | A |
\n(b) | A |\u00b2
\n(c) | A |\u00b3
\n(d) 3 | A |
\nSolution:
\n\"Class
\nHence option (b) is correct.<\/p>\n

\"NCERT<\/p>\n

Class 12 Maths Ex 4.5 NCERT Solutions Question 18.<\/strong>
\nIf A is an invertible matrix of order 2, then det. (A-1<\/sup>) is equal to:
\n(a) det. (A)
\n(b) \\(\\\\ \\frac { 1 }{ det.(A) } \\)
\n(c) 1
\n(d) 0
\nSolution:
\n|A|\u22600
\n\u21d2 A-1<\/sup> exists \u21d2 A-1<\/sup> = I
\n|AA-1<\/sup>| = |I| = I
\n\u21d2 |A||A-1<\/sup>| = I
\n\\(|{ A }^{ -1 }|=\\frac { 1 }{ |A| } \\)
\nHence option (b) is correct.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.5 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-5\/ NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.5 Ex 4.5 Class 12 NCERT Solutions Question 1. Solution: Let A = Adj A = Exercise 4.5 Class 12 NCERT …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.5<\/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 4 Determinants Ex 4.5 - MCQ Questions<\/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:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-5\/\" \/>\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 4 Determinants Ex 4.5 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.5 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-5\/ NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.5 Ex 4.5 Class 12 NCERT Solutions Question 1. 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