Question

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

Answer 1

AB = A + B
`[(3, 0),(0, 4)][(a, b),(0, c)] = [(3, 0),(0, 4)] + [(a, b),(0, c)]`
`[(3a , 3b),(0, 4c)] = [(3 + a, b),(0 , 4 + c)]`
3a = 3 + a
2a = 3
a = `(3)/(2)`
3b = b
2b = 0
b = 0
4c = 4 + c
3c = 4
c = `(4)/(3)`.