Question

If A = `[(1, 2, 2),(-3, -1, 0)], B = [(1, 0, 1),(2, 1, 3)]`, find the matrix C such that A + B + C is a zero matrix.

Answer 1

Find A + B

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

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

Use the condition for a zero matrix,

A + B + C = 0

C = −(A + B)

Find C

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

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