Question

If matrix X = `[(-3, 4),(2, -3)][(2),(-2)]` and 2X – 3Y = `[(10),(-8)]`, find the matrix ‘X’ and matrix ‘Y’.

Answer 1

Given: X = `[(-3, 4),(2, -3)][(2),(-2)]`

= `[(-3 xx 2 + 4 xx (-2)),(2 xx 2 + (-3)(-2))]`

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

= `[(-14),(10)]`

Let Y = `[(a),(b)]_(2 xx 1)`

∴ 2X – 3Y = `2[(-14),(10)] - 3[(a),(b)]`

= `[(-28),(20)] - [(3a),(3b)]`

= `[(-28 - 3a),(20 - 3b)]`

∴ `[(-28 - 3a),(20 - 3b)] = [(10),(-8)]`

∴ Comparing the elements, we have

–28 – 3a = 10

`\implies` –3a = 10 + 28

`\implies` –3a = 38

`\implies a = -38/3` and 20 – 3b = – 8

`\implies` –3b = – 8 – 20 = –28

∴ `b = 28/3`

∴ Y = `[(a),(b)]`

= `[((-38)/3),(28/3)]`

= `1/3 [(-38),(28)]`