Let A = 1 - 1 2 - 1 and B = a 1 b - 1 are two matrices. If A + B 2 = A 2 + B 2 , then the value of 3 a + 4 b is equal to

Question

Let A = 1 - 1 2 - 1 and B = a 1 b - 1 are two matrices. If A + B 2 = A 2 + B 2 , then the value of 3 a + 4 b is equal to, 15, 17, 19, 21

MARKS App · Accepted Answer

Given, A + B 2 = A 2 + B 2 A 2 + B 2 + A B + B A = A 2 + B 2 ⇒ A B + B A = O A B = 1 - 1 2 - 1 a 1 b - 1 = a - b 2 2 a - b 3 B A = a 1 b - 1 1 - 1 2 - 1 = a + 2 - a - 1 b - 2 - b + 1 A B + B A = 2 a - b + 2 - a + 1 2 a - 2 - b + 4 = O 2 a - b + 2 = 0 - a + 1 = 0 ⇒ a = 1 2 a - 2 = 0 ⇒ a = 1 - b + 4 = 0 ⇒ b = 4

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