Solveeit Logo
Login

Question

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]\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}. [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}