Question:
Consider two matrices: \( P = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix} \) and \( Q = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \). Which of the following statements is/are true?
Consider two matrices: \( P = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix} \) and \( Q = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \). Which of the following statements is/are true?
Updated On: Jul 12, 2024
- P and Q have same set of eigenvalues
- eigenvalues P and Q commute with each other
- P and Q have different sets of linearly independent eigenvectors
- P is diagonalizable
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The Correct Option is A, B, C
Solution and Explanation
The correct Answers are (A) :P and Q have same set of eigenvalues (B):eigenvalues P and Q commute with each other (C):P and Q have different sets of linearly independent eigenvectors
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