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)]`

Answer 1

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)]`.