Question

If A = `[(2, 1),(1, 3)]` and B = `[(3),(-11)]`, find the matrix X such that AX = B.

Answer 1

Let the order of the matrix X be a × b

AX = B

`[(2, 1),(1, 3)]_(2 xx 2) xx X_(a xx b) = [(3),(-11)]_(2 xx 1)`

Clearly, the order of the matrix X is 2 × 1.

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

`[(2, 1),(1, 3)] xx [(x),(y)] = [(3),(-11)]`

`[(2x + y),(x + 3y)] = [(3),(-11)]`

Comparing the two matrices, we get,

2x + y = 3  ...(1)

x + 3y = –11  ...(2)

Multiplying (1) with 3, we get,

6x + 3y = 9  ...(3)

Subtracting (2) from (3), we get,

5x = 20

x = 4

From (1), we have

y = 3 – 2x

= 3 – 8

= –5

∴ `X = [(4),(-5)]`