Question:
The values of \( \mu \) which satisfy the equation \( A^{100} \vec{x} = \mu \vec{x} \), where \( A = \begin{bmatrix} 2 & -1 \\ 0 & -2 \\ 1 & 1 \end{bmatrix} \) are
The values of \( \mu \) which satisfy the equation \( A^{100} \vec{x} = \mu \vec{x} \), where \( A = \begin{bmatrix} 2 & -1 \\ 0 & -2 \\ 1 & 1 \end{bmatrix} \) are
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Eigenvalues of a matrix give us the scaling factor for the corresponding eigenvector in the equation \( A \vec{x} = \mu \vec{x} \).
Updated On: May 5, 2025
- \( 0, 0, 0 \)
- \( 1, 1, 1 \)
- \( -1, -1, 1 \)
- \( 0, 1, 1 \)
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The Correct Option is D
Solution and Explanation
To solve for \( \mu \), we look for the eigenvalues of the matrix \( A \). After performing the necessary operations to find the eigenvalues, we obtain the values \( 0, 1, 1 \). These values of \( \mu \) satisfy the equation.
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