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


Question 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&𝑐1@𝑎2&𝑏2&𝑐2@𝑎3&𝑏3&𝑐3)]_(3 × 3) We need to find |kA| kA = k [■8(𝑎1&𝑏1&𝑐1@𝑎2&𝑏2&𝑐2@𝑎3&𝑏3&𝑐3)] = [■8(𝒌𝑎1&𝒌𝑏1&𝒌𝑐1@𝒌𝑎2&𝒌𝑏2&𝒌𝑐2@𝒌𝑎3&𝒌𝑏3&𝒌𝑐3)] If a matrix is multiplied by a constant, then constant is multiplied to all elements of matrix |"kA" | = |■8(𝑘𝑎1&𝑘𝑏1&𝑘𝑐1@𝑘𝑎2&𝑘𝑏2&𝑘𝑐2@𝑘𝑎3&𝑘𝑏3&𝑘𝑐3)| Taking out k common from R1 R2 & R3 = k. k. k |■8(a1&b1&c1@a2&b2&c2@a3&b3&c3)| = k3 |■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, Social Science, Physics, Chemistry, Computer Science at Teachoo.