Question

If `"A" = [(1 , 2),(-2 , 3)], "B" = [(2 , 1),(2 , 3)] "C" = [(-3 , 1),(2 , 0)]` verify that
A(B + C) = AB + AC.

Answer 1

B + C = `[(2 , 1),(2 , 3)] + [(-3 , 1),(2 , 0)]`

= `[(2 - 3 , 1 + 1),(2 + 2 , 3 + 0)] = [(-1 , 2),(4 , 3)]`

A(B+ C) = `[(1 , 2),(-2 , 3)][(-1 , 2),(4 , 3)]`

= `[(-1 + 8 , 2 + 6),(2 + 12 , -4 + 9)] = [(7 , 8),(14 , 5)]`

Now AB = `[(6 , 7),(2 , 7)]`

AC = `[(1 , 2),(-2 , 3)][(-3 , 1),(2 , 0)]`

= `[(-3 + 4 , 1 + 0),(6 + 6 , -2 + 0)] = [( 1 , 1),(12 , -2)]`

AB + AC = `[(6 , 7),(2 , 7)] + [(1 , 1),(12 , -2)]`

= `[(6 + 1 , 7 + 1),(2 + 12 , 7 - 2)]`

AB + AC = `[(7 , 8),(14 , 5)]`
Hence A(B + C) = AB + AC.