Question

If A = `[(2, 5),(1, 3)]`, B = `[(4, -2),(-1, 3)]` and I is the identity matric of the same order and A^t is the transpose of matrix A, find A^t.B + BI.

Answer 1

Given A = `[(2, 5),(1, 3)]`, B = `[(4, -2),(-1, 3)]`

A^t = `[(2, 1),(5, 3)]`

A^t.B + BI = `[(2, 1),(5, 3)][(4, -2),(-1, 3)] + [(4, -2),(-1, 3)][(1, 0),(0, 1)]`

= `[(8 - 1, -4 + 3),(20 - 3, -10 + 9)] + [(4 + 0, 0 - 2),(-1 + 0, 0 + 3)]`

= `[(7, -1),(17, -1)] + [(4, -2),(-1, 3)]`

= `[(7 + 4, -1 - 2),(17 - 1, -1 + 3)]`

= `[(11, -3),(16, 2)]`