Question:
Let $M =\begin{bmatrix} \alpha & β 6 \\-1 & -1 \end{bmatrix}, \alpha\, \epsilon\, R $ be a 2 Γ 2 matrix. If the eigenvalues of $M$ are $\beta$ and 4, then which of the following is/are CORRECT?
Let $M =\begin{bmatrix} \alpha & β 6 \\-1 & -1 \end{bmatrix}, \alpha\, \epsilon\, R $ be a 2 Γ 2 matrix. If the eigenvalues of $M$ are $\beta$ and 4, then which of the following is/are CORRECT?
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Updated On: Oct 1, 2024
- $\alpha + \beta = 1$
- An eigenvector corresponding to $\beta$ is $[2, 1]^T$
- The rank of the matrix M is 2
- The matrix $M^2$ + M is invertible
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The Correct Option is A, B, C
Solution and Explanation
The correct Options are A and B and C :$\alpha + \beta = 1$ AND An eigenvector corresponding to $\beta$ is $[2, 1]^T$ AND The rank of the matrix M is 2
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