If B 0 = - 4 - 3 - 3 1 0 1 4 4 3 , B n = a d j B n - 1 , ∀ n ∈ N and I is an identity matrix of order 3 , then B 1 + B 3 + B 5 + B 7 + B 9 is equal to

Question

If B 0 = - 4 - 3 - 3 1 0 1 4 4 3 , B n = a d j B n - 1 , ∀ n ∈ N and I is an identity matrix of order 3 , then B 1 + B 3 + B 5 + B 7 + B 9 is equal to, B 0, 5 B 0, 25 B 0, 5 I

MARKS App · Accepted Answer

B 0 2 = B 0 B 0 = - 4 - 3 - 3 1 0 1 4 4 3 - 4 - 3 - 3 1 0 1 4 4 3 ⇒ B 0 B 0 = 1 0 0 0 1 0 0 0 1 = I = B 0 - 1 B 0 Also, B 0 = 1 B 1 = a d j B 0 = B 0 B 0 - 1 = B 0 B 2 = a d j B 1 = B 0 B 3 = B 5 = B 7 = B 9 = B 0 Hence, B 1 + B 3 + B 5 + B 7 + B 9 = 5 B 0

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