Question

If A = `[(1, 0),(1"/"2, 1)]`, the A⁵⁰ is:

Options

• `[(1, 0),(0, 50)]`

• `[(1, 0),(50, 1)]`

• `[(1, 25),(0, 1)]`

• None of these

Answer 1

None of these

Explanation:

We have

`A^2 = [(1, 0),(1"/"2, 1)] [(1, 0),(1"/"2, 1)] = [(1, 0),(2(1"/"2), 1)] = [(1, 0),(1, 1)]`

`A^4 = [(1, 0),(1, 1)] [(1, 0),(1, 1)] = [(1, 0),(2, 1)]`

`A^8 = [(1, 0),(2, 1)] [(1, 0),(2, 1)] = [(1, 0),(4, 1)]`

In general, by induction Aⁿ = `[(1, 0),(n"/"2, 1)]`

= `A^50 = [(1, 0),(25, 1)]`