Question

Answer the following question:

If A = `[(2, 1, -3),(0, 2, 6)]`, B = `[(1, 0, -2),(3, -1, 4)]`, find AB^T and A^TB

Answer 1

A = `[(2, 1, -3),(0, 2, 6)]`, B = `[(1, 0, -2),(3, -1, 4)]`

∴ A^T = `[(2, 0),(1, 2),(-3, 6)]` and B^T = `[(1, 3),(0, -1),(-2, 4)]`

∴ AB^T = `[(2, 1, -3),(0, 2, 6)] [(1, 3),(0, -1),(-2, 4)]`

= `[(2 + 0 + 6, 6 - 1 - 12),(0 + 0 -12, 0 - 2 + 24)]`

= `[(8, -7),(-12, 22)]`

and A^TB = `[(2, 0),(1, 2),(-3, 6)] [(1, 0, -2),(3, -1, 4)]`

= `[(2 + 0, 0 + 0, -4 + 0),(1 + 6, 0 - 2, -2 + 8),(-3 + 18, 0 - 6, 6 + 24)]`

= `[(2, 0, -4),(7, -2, 6),(15, -6, 30)]`