Question

Given A = `[(2, -6),(2, 0)]`, B = `[(-3, 2),(4, 0)]` and C = `[(4, 0),(0, 2)]`. Find the matrix X such that A + 2X = 2B + C.

Answer 1

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

Let X = `[(x , y),(z, t)]`

A + 2X = 2B + C

2X = 2B + C – A

`2[(x, y),(z, t)] = 2[(-3, 2),(4, 0)] + [(4, 0),(0, 2)] - [(2, -6),(2, 0)]`

= `[(-6, 4),(8, 0)] + [(4, 0),(0, 2)] - [(2, -6),(2, 0)]`

= `[(-6 + 4 - 2, 4 + 0 + 6),(8 + 0 - 2, 0 + 2 - 0)]`

= `[(-4 , 10),(6, 2)]`

∴ `2[(x, y),(z, t)] = [(-4, 10),(6, 2)]`

∴ `[(x, y),(z, t)] = (1)/(2)[(-4, 10),(6, 2)]`

= `[(-2, 5),(3, 1)]`