Question 15 (MCQ) - Chapter 4 Class 12 Determinants (Important Question)

Last updated at December 16, 2024 by

Ex 4.2, 15 - Let A be a square matrix of order 3 x 3, then |kA|

Ex 4.2, 15 - Chapter 4 Class 12 Determinants - Part 2

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Question 15 Choose the correct answer. Let A be a square matrix of order 3 Ɨ 3, then |"kA" | is equal to A. "k" |"A" | B. "k" 2|"A" | C. "k" 3|"A" | D. 3"k" |"A" | Let A = [ā– 8(š‘Ž1&š‘1&š‘1@š‘Ž2&š‘2&š‘2@š‘Ž3&š‘3&š‘3)]_(3 Ɨ 3) We need to find |kA| kA = k [ā– 8(š‘Ž1&š‘1&š‘1@š‘Ž2&š‘2&š‘2@š‘Ž3&š‘3&š‘3)] = [ā– 8(š’Œš‘Ž1&š’Œš‘1&š’Œš‘1@š’Œš‘Ž2&š’Œš‘2&š’Œš‘2@š’Œš‘Ž3&š’Œš‘3&š’Œš‘3)] If a matrix is multiplied by a constant, then constant is multiplied to all elements of matrix |"kA" | = |ā– 8(š‘˜š‘Ž1&š‘˜š‘1&š‘˜š‘1@š‘˜š‘Ž2&š‘˜š‘2&š‘˜š‘2@š‘˜š‘Ž3&š‘˜š‘3&š‘˜š‘3)| Taking out k common from R1 R2 & R3 = k. k. k |ā– 8(a1&b1&c1@a2&b2&c2@a3&b3&c3)| = k3 |ā– 8(a1&b1&c1@a2&b2&c2@a3&b3&c3)| = k3 |A| Thus, Correct answer is C Property: If each element of row of determinant is multiplied by a constant k , then its value get multiplied by k

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo