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Question 6

If A = [3 1 -1 2] and I = [1 0 0 1], find k so that A 2 = 5A + kI

If A = [3 1 -1 2] and I = [1 0 0 1], find k so that A^2 = 5A + kI

Question 6 - CBSE Class 12 Sample Paper for 2019 Boards - Part 2
Question 6 - CBSE Class 12 Sample Paper for 2019 Boards - Part 3

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Question 6 If A = [■8(3&[email protected]−1&2)] and I = [■8(1&[email protected]&1)], find k so that A2 = 5A + kI Finding A2 A2 = [■8(3&[email protected]−1&2)] [■8(3&[email protected]−1&2)] A2 = [■8(3(3)+1(−1)&3(1)+1(2)@−1(3)+2(−1)&−1(1)+2(2))] A2 = [■8(9−1&[email protected]−3−2&−1+4)] A2 = [■8(8&[email protected]−5&3)] Finding 5A 5A = 5[■8(3&[email protected]−1&2)] 5A = [■8(5×3&5×[email protected]×(−1)&5×2)] 5A = [■8(15&[email protected]−5&10)] Now, our equation is A2 = 5A + kI Putting values [■8(8&[email protected]−5&3)] = [■8(15&[email protected]−5&10)] + k [■8(1&[email protected]&1)] [■8(8&[email protected]−5&3)] = [■8(15&[email protected]−5&10)] + [■8(𝑘×1&𝑘×[email protected]𝑘×0&𝑘×1)] [■8(8&[email protected]−5&3)] = [■8(15&[email protected]−5&10)] + [■8(𝑘&[email protected]&𝑘)] [■8(8&[email protected]−5&3)] = [■8(15+𝑘&[email protected]−5+0&10+𝑘)] [■8(8&[email protected]−5&3)] = [■8(15+𝑘&[email protected]−5&10+𝑘)] Thus, 8 = 15 + k 8 – 15 = k –7 = k k = –7

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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.