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