Check sibling questions

Ex 3.2, 17 - Find k so that  A2 = kA - 2I, if A = [3 -2 4 -2]

Ex 3.2, 17 - Chapter 3 Class 12 Matrices - Part 2
Ex 3.2, 17 - Chapter 3 Class 12 Matrices - Part 3


Transcript

Ex 3.2, 17 If A = [■8(3&−[email protected]&−2)] and I= [■8(1&[email protected]&1)] , find k so that A2 = kA – 2I Finding A2 A2 = A × A = [■8(3&−[email protected]&−2)][■8(3&−[email protected]&−2)] = [■8(3(3)+(−2)(4)&3(−2)+(−2)(−2)@4(3)+(−2)(4)&4(−2)+(−2)(−2))] = [■8(9−8&−[email protected]−8&−8+4)] = [■8(1&−[email protected]&−4)] ∴ A2 = [■8(1&−[email protected]&−4)] Now , given that A2 = kA – 2I Putting values [■8(1&−[email protected]&−4)] = k [■8(3&−[email protected]&−2)] − 2 [■8(1&[email protected]&1)] [■8(1&−[email protected]&−4)] = [■8(3k&−[email protected]&−2k)] − [■8(1×2&0×[email protected]×2&1×2)] [■8(1&−[email protected]&−4)] = [■8(3k&−[email protected]&−2k)] − [■8(2&[email protected]&2)] [■8(1&−[email protected]&−4)] = [■8(3k−2&−2k−[email protected]−0&−2k−2)] [■8(1&−[email protected]&−4)] = [■8(3k−2&−[email protected]&−2k−2)] Since matrices are equal. Comparing its corresponding elements. 1 = 3k – 2 1 + 2 = 3k 3 = 3k 3/3 = k 1 = k k = 1 Thus, k = 1

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.