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Ex 4.5
Ex 4.5, 2
Ex 4.5, 3 Important
Ex 4.5, 4 Important
Ex 4.5, 5
Ex 4.5, 6 Important
Ex 4.5, 7
Ex 4.5, 8
Ex 4.5, 9
Ex 4.5, 10 Important
Ex 4.5, 11 Important
Ex 4.5, 12
Ex 4.5, 13
Ex 4.5, 14 Important You are here
Ex 4.5, 15 Important
Ex 4.5, 16
Ex 4.5, 17 (MCQ) Important
Ex 4.5, 18 (MCQ) Important
Last updated at March 30, 2023 by Teachoo
Ex 4.5, 14 For the matrix A = [■8(3&[email protected]&1)] , find the numbers a and b such that A2 + aA + bI = O. Finding A2 A2 = A.A = [■8(3&[email protected]&1)] [■8(3&[email protected]&1)] = [■8(3(3)+2(1)&3(2)+2(1)@1(3)+1(1)&1(2)+1(1))] = [■8(9+2&[email protected]+1&2+1)] = [■8(11&[email protected]&3)] Now, A2 + aA + bI = O Putting values [■8(11&[email protected]&3)] + a [■8(3&[email protected]&1)] + b [■8(1&[email protected]&1)] = O [■8(11&[email protected]&3)] + [■8(3a&[email protected]&a)] + [■8(b&[email protected]&b)] = O [■8(11+3a+b&[email protected]+a+0&3+a+b)] = O [■8(3a+b+11&[email protected]+a&a+b+3)] = [■8(0&[email protected]&0)] Since the matrices are equal, Comparing corresponding elements 3a + b + 11 = 0 2a + 8 = 0 4 + a = 0 a + b + 3 = 0 Solving (3) a + 4 = 0 a = –4 Putting value a in (1) 11 + 3 a + b = 0 11 + 3 (–4) + b = 0 11 – 12 +b = 0 –1 + b = 0 …(1) b = 1 Hence, a = −4, b = 1