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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise

Transcript

Ex 4.2, 15 Choose the correct answer. Let A be a square matrix of order 3 ร— 3, then |"kA" | is equal to A. "k" |"A" | B. "k" 2|"A" | C. "k" 3|"A" | D. 3"k" |"A" | Let A = [โ– 8(๐‘Ž1&๐‘1&๐‘1@๐‘Ž2&๐‘2&๐‘2@๐‘Ž3&๐‘3&๐‘3)]_(3 ร— 3) We need to find |kA| kA = k [โ– 8(๐‘Ž1&๐‘1&๐‘1@๐‘Ž2&๐‘2&๐‘2@๐‘Ž3&๐‘3&๐‘3)] = [โ– 8(๐’Œ๐‘Ž1&๐’Œ๐‘1&๐’Œ๐‘1@๐’Œ๐‘Ž2&๐’Œ๐‘2&๐’Œ๐‘2@๐’Œ๐‘Ž3&๐’Œ๐‘3&๐’Œ๐‘3)] If a matrix is multiplied by a constant, then constant is multiplied to all elements of matrix |"kA" | = |โ– 8(๐‘˜๐‘Ž1&๐‘˜๐‘1&๐‘˜๐‘1@๐‘˜๐‘Ž2&๐‘˜๐‘2&๐‘˜๐‘2@๐‘˜๐‘Ž3&๐‘˜๐‘3&๐‘˜๐‘3)| Taking out k common from R1 R2 & R3 = k. k. k |โ– 8(a1&b1&c1@a2&b2&c2@a3&b3&c3)| = k3 |โ– 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

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.