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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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Ex 4.2, 15 Choose the correct answer. Let A be a square matrix of order 3 × 3, then |"kA" | is equal to A. "k" |"A" | B. "k" 2|"A" | C. "k" 3|"A" | D. 3"k" |"A" | Let A = [■8(𝑎1&𝑏1&𝑐[email protected]𝑎2&𝑏2&𝑐[email protected]𝑎3&𝑏3&𝑐3)]_(3 × 3) We need to find |kA| kA = k [■8(𝑎1&𝑏1&𝑐[email protected]𝑎2&𝑏2&𝑐[email protected]𝑎3&𝑏3&𝑐3)] = [■8(𝒌𝑎1&𝒌𝑏1&𝒌𝑐[email protected]𝒌𝑎2&𝒌𝑏2&𝒌𝑐[email protected]𝒌𝑎3&𝒌𝑏3&𝒌𝑐3)] If a matrix is multiplied by a constant, then constant is multiplied to all elements of matrix |"kA" | = |■8(𝑘𝑎1&𝑘𝑏1&𝑘𝑐[email protected]𝑘𝑎2&𝑘𝑏2&𝑘𝑐[email protected]𝑘𝑎3&𝑘𝑏3&𝑘𝑐3)| Taking out k common from R1 R2 & R3 = k. k. k |■8(a1&b1&[email protected]&b2&[email protected]&b3&c3)| = k3 |■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.