12th Maths Chapter 4 Exercise 4.1 Question 2.<\/strong> \n(i) \\(\\begin{vmatrix} cos\\theta & \\quad -sin\\theta \\\\ sin\\theta & \\quad cos\\theta \\end{vmatrix}\\) \n(ii) \\(\\begin{vmatrix} { x }^{ 2 }-x+1 & x-1 \\\\ x+1 & x+1 \\end{vmatrix}\\) \nSolution: \n(i) \\(\\begin{vmatrix} cos\\theta & \\quad -sin\\theta \\\\ sin\\theta & \\quad cos\\theta \\end{vmatrix}\\) \n= cos\u03b8 cos\u03b8 – (sin\u03b8)(-sin\u03b8) \n= cos\u00b2\u03b8 + sin\u00b2\u03b8 \n= 1<\/p>\n(ii) \\(\\begin{vmatrix} { x }^{ 2 }-x+1 & x-1 \\\\ x+1 & x+1 \\end{vmatrix}\\) \n= (x\u00b2 – x + 1) (x + 1) – (x + 1) (x – 1) \n= x\u00b3 – x\u00b2 + x + x\u00b2 – x + 1 – x\u00b2 + 1 \n= x\u00b3 – x\u00b2 + 2<\/p>\n
Question 3. \nIf \\(A=\\begin{bmatrix} 1 & 2 \\\\ 4 & 2 \\end{bmatrix}\\) then show that |2A|=|4A| \nSolution: \n\\(A=\\begin{bmatrix} 1 & 2 \\\\ 4 & 2 \\end{bmatrix}\\) \n\u21d2 \\(2A=\\begin{bmatrix} 2 & 4 \\\\ 8 & 4 \\end{bmatrix}\\) \nL.H.S = |2A| \n= \\(2A=\\begin{bmatrix} 2 & 4 \\\\ 8 & 4 \\end{bmatrix}\\) \n= – 24 \n4|A| = 4|\\(\\left|\\begin{array}{ll} 1 & 2 \\\\ 4 & 2 \\end{array}\\right|\\)| = 4(2 – 8) = 4 x – 6 = – 24 \n\u2234 |2A| = 4|A|<\/p>\n
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Question 4. \n\\(A=\\left[ \\begin{matrix} 1 & 0 & 1 \\\\ 0 & 1 & 2 \\\\ 0 & 0 & 4 \\end{matrix} \\right] \\) , then show that |3A| = 27|A| \nSolution: \n <\/p>\n
Question 5. \nEvaluate the following determinant: \n(i) \\(\\left| \\begin{matrix} 3 & -1 & -2 \\\\ 0 & 0 & -1 \\\\ 3 & -5 & 0 \\end{matrix} \\right| \\) \n(ii) \\(\\left| \\begin{matrix} 3 & -4 & 5 \\\\ 1 & 1 & -2 \\\\ 2 & 3 & 1 \\end{matrix} \\right| \\) \n(iii) \\(\\left| \\begin{matrix} 0 & 1 & 2 \\\\ -1 & 0 & -3 \\\\ -2 & 3 & 0 \\end{matrix} \\right| \\) \n(iv) \\(\\left| \\begin{matrix} 2 & -1 & -2 \\\\ 0 & 2 & -1 \\\\ 3 & -5 & 0 \\end{matrix} \\right| \\) \nSolution: \n(i) \\(\\left| \\begin{matrix} 3 & -1 & -2 \\\\ 0 & 0 & -1 \\\\ 3 & -5 & 0 \\end{matrix} \\right| \\) \n <\/p>\n
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Question 6. \nIf \\(\\left[ \\begin{matrix} 1 & 1 & -2 \\\\ 2 & 1 & -3 \\\\ 5 & 4 & -9 \\end{matrix} \\right] \\), find |A| \nSolution: \n|A| = \\(\\left[ \\begin{matrix} 1 & 1 & -2 \\\\ 2 & 1 & -3 \\\\ 5 & 4 & -9 \\end{matrix} \\right] \\) \n= 1(-9+12)-1(-18+15)-2(8-5) \n= 0<\/p>\n
Question 7. \nFind the values of x, if \n(i) \\(\\begin{vmatrix} 2 & 4 \\\\ 5 & 1 \\end{vmatrix}=\\begin{vmatrix} 2x & 4 \\\\ 6 & x \\end{vmatrix}\\) \n(ii)\\(\\begin{vmatrix} 2 & 3 \\\\ 4 & 5 \\end{vmatrix}=\\begin{vmatrix} x & 3 \\\\ 2x & 5 \\end{vmatrix}\\) \nSolution: \n(i) \\(\\begin{vmatrix} 2 & 4 \\\\ 5 & 1 \\end{vmatrix}=\\begin{vmatrix} 2x & 4 \\\\ 6 & x \\end{vmatrix}\\) \n\u21d2 2 – 20 = 2x\u00b2 – 24 \n\u21d2 x\u00b2 = 3 \n\u21d2 x = \u00b1\\(\\sqrt{3}\\)<\/p>\n
(ii) \\(\\begin{vmatrix} 2 & 3 \\\\ 4 & 5 \\end{vmatrix}=\\begin{vmatrix} x & 3 \\\\ 2x & 5 \\end{vmatrix}\\) \nor \n2 \u00d7 5 – 4 \u00d7 3 = 5 \u00d7 x – 2x \u00d7 3 \n\u21d2 x = 2<\/p>\n
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Question 8. \nIf \\(\\begin{vmatrix} x & 2 \\\\ 18 & x \\end{vmatrix}=\\begin{vmatrix} 6 & 2 \\\\ 18 & 6 \\end{vmatrix}\\), then x is equal to \n(a) 6 \n(b) +6 \n(c) -6 \n(d) 0 \nSolution: \n(b) \\(\\begin{vmatrix} x & 2 \\\\ 18 & x \\end{vmatrix}=\\begin{vmatrix} 6 & 2 \\\\ 18 & 6 \\end{vmatrix}\\) \n\u21d2 x\u00b2 – 36 = 36 – 36 \n\u21d2 x\u00b2 = 36 \n\u21d2 x = \u00b1 6<\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-4-ex-4-1\/ NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.1 Class 12 Maths Chapter 4 Exercise 4.1 Solutions Question 1. Evaluate the following determinant: Solution: = 2 x (- 1) …<\/p>\n
NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.1<\/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 4 Determinants Ex 4.1 - 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