Question

Given A = `[(3, 0),(0, 4)]`, B = `[(a, b),(0, c)]` and that AB = A + B; find the values of a, b and c.

Answer 1

AB = `[(3, 0),(0, 4)][(a, b),(0, c)]`

= `[(3 xx  a + 0 xx 0, 3 xx b + 0 xx c),(0 xx a + 4 xx 0, 0 xx b + 4 xx c)]`

= `[(3a + 0, 3b + 0),(0 + 0, 0 + 4c)]`

= `[(3a, 3b),(0, 4c)]`

A + B = `[(3, 0),(0, 4)] + [(a, b),(0, c)]`

= `[(3 + a, 0 + b),(0 + 0, 4 + c)]`

Given, AB = A + B

`∴ [(3a, 3b),(0, 4c)] = [(3 + a, b),(0, 4 + c)]`

Comparing the corresponding elements, we get,

3a = 3 + a

`=>` 3a – a = 3

`=>` 2a = 3

`=> a = 3/2`

3b = b

`=>` 3b – b = 0

`=>` 2b = 0

`=>` b = 0

4c = 4 + c

`=>` 3c = 4

`=> c = 4/3`