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Question: If X = \(\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}\), then X<sup>n</sup>, for n Ī N, is equal to ...

If X = [1111]\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}, then Xn, for n Ī N, is equal to –

A

2n–1 X

B

n2X

C

nX

D

2n+1 X

Answer

2n–1 X

Explanation

Solution

\Xn= [2n–12n–12n–12n–1]\begin{bmatrix} 2^{n–1} & 2^{n–1} \\ 2^{n–1} & 2^{n–1} \end{bmatrix} Ž Xn = 2n–1. [1111]\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}