If A is a symmetric matrix and B is skew- symmetric matrix such that A + B = 2 3 5 - 1 , then A B is equal to:

Question

If A is a symmetric matrix and B is skew- symmetric matrix such that A + B = 2 3 5 - 1 , then A B is equal to:, - 4 2 1 4, 4 - 2 1 - 4, 4 - 2 - 1 - 4, - 4 - 2 - 1 4

MARKS App · Accepted Answer

Given A is symmetric and B is skew symmetric, hence A = a b b c and B = 0 d - d 0 Now A + B = a b + d b - d c = 2 3 5 - 1 ⇒ a = 2 , b = 4 , c = - 1 and d = - 1 ⇒ A = 2 4 4 - 1 and B = 0 - 1 1 0 Hence A B = 2 4 4 - 1 0 - 1 1 0 = 4 - 2 - 1 - 4

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