Question

If A = `[(0, -1),(4, -3)]`, B = `[(-5),(6)]` and 3A × M = 2B; find matrix M.

Answer 1

Let the order of matrix M be a × b.

3A × M = 2B

`3[(0, -1),(4, -3)]_(2xx2) xx M_(a xx b) = 2[(-5), (6)]_(2 xx 1)`

Clearly, the order of matrix M is 2 × 1

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

Then,

`3[(0, -1),(4, -3)] xx [(x),(y)] = 2[(-5),(6)]`

`[(0, -3),(12, -9)] xx [(x),(y)] = [(-10),(12)]`

`[(0 xx x + (-3)y),(12 xx x + (-9)y)] = [(-10),(12)]`

`[(0 - 3y),(12x - 9y)] = [(-10),(12)]`

`[(-3y),(12x - 9y)] = [(-10),(12)]`

Comparing the corresponding elements, we get

∴ –3y = –10

`=> y = 10/3`

12x – 9y = 12

`=> 12x - (9 xx 10)/3 = 12`

`=>` 12x – 30 = 12

`=>` 12x = 12 + 30

`=>` 12x = 42

∴ `x = 42/12 = 7/2`

∴ `M = [(7/2),(10/3)]`