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Let A = 1 - 1 0 0 1 - 1 0 0 1 and B = 7 A 20 - 20 A 7 + 2 I , where I is an identity matrix of order 3 × 3 . If B = b i j , then b 13 is equal to

Correct answer

0

Step-by-step solution

Let A = 1 - 1 0 0 1 - 1 0 0 1 = I + C where I = 1 0 0 0 1 0 0 0 1 ,   C = 0 - 1 0 0 0 - 1 0 0 0 Then, C 2 = 0 0 1 0 0 0 0 0 0 , C 3 = 0 0 0 0 0 0 0 0 0 = C 4 = C 5 = … … . Now, B = 7   A 20 - 20   A 7 + 2 I = 7 ( I + C ) 20 - 20 ( I + C ) 7 + 2 I = 7 I + 20 C + C 2 20 C 2 + . . . - 20 I + 7 C + C 2 7 C 2 + . . + 2 I = – 11 I + 910   C 2 = - 11 0 910 0 - 11 0 0 0 - 11 So, b 13 = 910

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