Question

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

Answer 1

A + B + C = 0

C = −(A + B)

Find A + B:

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

= `((3, 4),(3, 3),(4, 0))`

Find C:

C = `-((3, 4),(3, 3),(4, 0))`

= `((-3, -4),(-3, -3),(-4, 0))`