Question:
Consider the \(2 \times 2\) matrix \( M = \begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix} \in M_2(\mathbb{R}) \). If the eighth power of \( M \) satisfies \( M^8 \begin{pmatrix} 1 \\ 1 \end{pmatrix} = \begin{pmatrix} x \\ y \end{pmatrix} \), then the value of \( x \) is
Consider the \(2 \times 2\) matrix \( M = \begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix} \in M_2(\mathbb{R}) \). If the eighth power of \( M \) satisfies \( M^8 \begin{pmatrix} 1 \\ 1 \end{pmatrix} = \begin{pmatrix} x \\ y \end{pmatrix} \), then the value of \( x \) is
Updated On: Oct 1, 2024
- 21
- 22
- 34
- 35
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The Correct Option is C
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The correct option is (C): 34
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