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