{"id":29783,"date":"2023-11-01T17:36:15","date_gmt":"2023-11-01T12:06:15","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=29783"},"modified":"2023-11-02T14:34:41","modified_gmt":"2023-11-02T09:04:41","slug":"ncert-solutions-for-class-12-maths-chapter-4-ex-4-5","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/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.<\/p>\n

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

\"NCERT<\/p>\n

Question 1.
\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

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

Question 3.
\n\\(\\begin{bmatrix} 2 & 3 \\\\ -4 & 6 \\end{bmatrix}\\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

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

Question 5.
\n\\(\\begin{bmatrix} 2 & -2 \\\\ 4 & 3 \\end{bmatrix}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 6.
\n\\(\\begin{bmatrix} -1 & 5 \\\\ -3 & 2 \\end{bmatrix}\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 7.
\n\\(\\left[ \\begin{matrix} 1 & 2 & 3 \\\\ 0 & 2 & 4 \\\\ 0 & 0 & 5 \\end{matrix} \\right]\\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 8.
\n\\(\\left[ \\begin{matrix} 1 & 0 & 0 \\\\ 3 & 3 & 0 \\\\ 5 & 2 & -1 \\end{matrix} \\right]\\)
\nSolution:
\n\"NCERT<\/p>\n

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

Question 10.
\n\\(\\left[ \\begin{matrix} 1 & -1 & 2 \\\\ 0 & 2 & -3 \\\\ 3 & -2 & 4 \\end{matrix} \\right]\\)
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 11.
\n\\(\\left[ \\begin{matrix} 1 & 0 & 0 \\\\ 0 & cos\\alpha & sin\\alpha \\\\ 0 & sin\\alpha & -cos\\alpha \\end{matrix} \\right] \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 12.
\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\"NCERT<\/p>\n

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

\"NCERT<\/p>\n

Question 14.
\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\"NCERT<\/p>\n

Question 15.
\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\"NCERT
\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\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 16.
\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\"NCERT<\/p>\n

Question 17.
\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\"NCERT
\nHence option (b) is correct.<\/p>\n

\"NCERT<\/p>\n

Question 18.
\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. NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.5 Question 1. Solution: Let A = Adj A = Question 2. Solution: Question 3. Solution: Question 4. Solution: |A| = A11 …<\/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":{"spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.5 - 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-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 - NCERT Solutions\" \/>\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. 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