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Question: If A = \(\begin{bmatrix} 1 & 1/2 \\ 0 & 1 \end{bmatrix}\) then A<sup>64</sup> is :...

If A = [11/201]\begin{bmatrix} 1 & 1/2 \\ 0 & 1 \end{bmatrix} then A64 is :

A

[132321]\begin{bmatrix} 1 & 32 \\ 32 & 1 \end{bmatrix}

B

[10321]\begin{bmatrix} 1 & 0 \\ 32 & 1 \end{bmatrix}

C

[13201]\begin{bmatrix} 1 & 32 \\ 0 & 1 \end{bmatrix}

D

None

Answer

[13201]\begin{bmatrix} 1 & 32 \\ 0 & 1 \end{bmatrix}

Explanation

Solution

A2 = [11/201]\begin{bmatrix} 1 & 1/2 \\ 0 & 1 \end{bmatrix} [11/201]\begin{bmatrix} 1 & 1/2 \\ 0 & 1 \end{bmatrix} = [1101]\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}

A3 = [1101]\left[ \begin{array} { l l } 1 & 1 \\ 0 & 1 \end{array} \right] [11/201]\begin{bmatrix} 1 & 1/2 \\ 0 & 1 \end{bmatrix} = [13/201]\begin{bmatrix} 1 & 3/2 \\ 0 & 1 \end{bmatrix}

\ A64 = [13201]\begin{bmatrix} 1 & 32 \\ 0 & 1 \end{bmatrix}