Question

If `[(-1, 0),(2, 5)] x = [(-2),(9)]`, write

1. the order of matrix X
2. the matrix X

Answer 1

(i)

Let matrix X be of order a × b

`[(-1, 0),(2, 5)]_(2 xx 2) . X_(a xx b) = [(-2),(9)]_(2 xx 1)`

So,

a = 2, b = 1

∴ Order of matrix X is 2 × 1

(ii)

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

⇒ `[(-1, 0),(2, 5)] . [(x),(y)] = [(-2),(9)]`

⇒ `[(-1 xx x + 0 xx y),(2 xx x + 5 xx y)] = [(-2),(9)]`

⇒ `[(-x),(2x + 5y)] = [(-2),(9)]`

−x = −2 

x = 2   ...(1)

2x + 5y = 9   ...(2)

Substitute x = 2 into (2):

2x + 5y = 9

2(2) + 5y = 9

4 + 5y = 9

5y = 9 − 4

5y = 5

y = `5/5`

y = 1

∴ The matrix X = `[(2),(1)]`