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

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

Question 6 - CBSE Class 12 Sample Paper for 2019 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards