Question

Let $M =\begin{bmatrix} \alpha & − 6 \\\\-1 & -1 \end{bmatrix}, \alpha\, \epsilon\, R$ be a 2 × 2 matrix. If the eigenvalues of $M$ are $\beta$ and 4, then which of the following is/are CORRECT?

• A. $\alpha + \beta = 1$
• B. An eigenvector corresponding to $\beta$ is $[2, 1]^T$
• C. The rank of the matrix M is 2
• D. The matrix $M^2$ + M is invertible

Answer 1

Answer: (A), (B), (C)

$\alpha + \beta = 1$

Answer 2

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