For two 3 × 3 matrices A and B , let A + B = 2 B ' and 3 A + 2 B = I 3 , where B ′ is the transpose of B and I 3 is 3 × 3 identity matrix. Then :

Step-by-step solution

Given A + B = 2 B T ⇒ A T + B T = 2 B ⇒           B = A T + B T 2 = A + B T + A T 2 = 2 B T 2 A + A T = 3 B T ⇒           A = 3 B T - A T 2 3 A + 2 B = I 3 ...... i ⇒             3 3 B T - A T 2 + 2 A T + B T 2 = I 3 ⇒         3 B T + 2 B T 2 + 2 A T + B T 2 = I 3 ⇒             11 B T - A T = 2 I 3 ....... i i Equation i + i i 35 B = 7 I 3 ⇒ &#16