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Question 15 (MCQ) - Verifying properties of a determinant - Chapter 4 Class 12 Determinants

Last updated at May 29, 2023 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 Γ— 3, then |"kA" | is equal to A. "k" |"A" | B. "k" 2|"A" | C. "k" 3|"A" | D. 3"k" |"A" | Let A = [β– 8(π‘Ž1&𝑏1&𝑐1@π‘Ž2&𝑏2&𝑐2@π‘Ž3&𝑏3&𝑐3)]_(3 Γ— 3) We need to find |kA| kA = k [β– 8(π‘Ž1&𝑏1&𝑐1@π‘Ž2&𝑏2&𝑐2@π‘Ž3&𝑏3&𝑐3)] = [β– 8(π’Œπ‘Ž1&π’Œπ‘1&π’Œπ‘1@π’Œπ‘Ž2&π’Œπ‘2&π’Œπ‘2@π’Œπ‘Ž3&π’Œπ‘3&π’Œπ‘3)] If a matrix is multiplied by a constant, then constant is multiplied to all elements of matrix |"kA" | = |β– 8(π‘˜π‘Ž1&π‘˜π‘1&π‘˜π‘1@π‘˜π‘Ž2&π‘˜π‘2&π‘˜π‘2@π‘˜π‘Ž3&π‘˜π‘3&π‘˜π‘3)| Taking out k common from R1 R2 & R3 = k. k. k |β– 8(a1&b1&[email protected]&b2&[email protected]&b3&c3)| = k3 |β– 8(a1&b1&[email protected]&b2&[email protected]&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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.