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Question

Linear Algebra Question on Matrices

Consider the 2×22 \times 2 matrix M=(11 10)M2(R)M = \begin{pmatrix} 1 & 1 \\\ 1 & 0 \end{pmatrix} \in M_2(\mathbb{R}). If the eighth power of MM satisfies M8(1 1)=(x y)M^8 \begin{pmatrix} 1 \\\ 1 \end{pmatrix} = \begin{pmatrix} x \\\ y \end{pmatrix}, then the value of xx is

A

21

B

22

C

34

D

35

Answer

34

Explanation

Solution

The correct option is (C): 34