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Question
Choose the correct answer from the given four options :
If A + B = `[(1, 0),(1, 1)]` and A – 2B = `[(-1, 1),(0, -1)]` then A is equal to
Options
`(1)/(3)[(1, 1),(2, 1)]`
`(1)/(3)[(2, 1),(1, 2)]`
`[(1, 1),(2, 1)]`
`[(2, 1),(1, 2)]`
Solution
A + B = `[(1, 0),(1, 1)]`
and
A – 2B = `[(-1, 1),(0, -1)]`
⇒ 2A + 2B = `[(2, 0),(2, 2)]` (Multiplying by 2)...(i)
A – 2B = `[(-1, 1),(0, -1)]` ...(ii)
Adding (i) and (ii), we get
3A = `[(2, 0),(2, 2)] + [(-1, 1),(0, -1)]`
= `[(1, 1),(2, 1)]`
∴ A = `(1)/(3)[(1, 1),(2, 1)]`.
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