Question

Given `[(2, 1),(-3,4)]` . X = `[(7),(6)]`. Write:

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

If `[(2, 1),(-3,4)]` . X = `[(7),(6)]`. Write:

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

Answer 1

Given `[(2,1),(-3,4)]` X = `[(7),(6)]`

i. Let the order of X be a × b

∴ `[(2, 1),(-3, 4)]_(2 xx 2) . X_(a xx b) = [(7),(6)]_(2 xx 1)`

`=>` a = 2 and b = 1

∴ The order of the matrix X = a × b = 2 × 1

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

∴ `[(2, 1),(-3, 4)][(x),(y)] = [(7),(6)]`

`=> [(2x + y),(-3x + 4y)] = [(7),(6)]`

2x + y = 7   ...(1)

–3x + 4y = 6  ...(2)

Multiplying (1) by 4 and subtracting from (2)

`=>` –11x = –22

`=> x = (-22)/(-11)`

= 2

Form (1),

y = 7 – 2x

= 7 – 2(2)

= 7 – 4

= 3

∴ The matrix `X = [(x),(y)] = [(2),(3)]`