Question

If A = `[(7, 3, 0),(0, 4, -2)], "B" = [(0, -2, 3),(2, 1, -4)]`, then find A^T + 4B^T.

Answer 1

A = `[(7, 3, 0),(0, 4, -2)]  "and"  "B" = [(0, -2, 3),(2, 1, -4)]`

∴ A^T = `[(7, 0),(3, 4),(0, -2)]  "and"  "B"^"T" = [(0, 2),(-2, 1),(3, -4)]`

A^T + 4B^T = `[(7, 0),(3, 4),(0, -2)] + 4[(0, 2),(-2, 1),(3, -4)]`

= `[(7, 0),(3, 4),(0, -2)] + [(0, 8),(-8, 4),(12, -16)]`

= `[(7 + 0, 0 + 8),(3 - 8, 4 + 4),(0 + 12, -2 - 16)]`

= `[(7, 8),(-5, 8),(12, -18)]`.