Question 1

Let $A = \begin{pmatrix} 2 & 1 & 1 \\ a & 3 & 2 \\ 3 & b & c \end{pmatrix}$ be a $3 \times 3$ matrix. Let $\alpha$ be the eigenvalue corresponding to the eigenvector $v_1 = \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix}$ and $\beta$ is the eigenvalue corresponding to the eigenvector $v_2 = \begin{pmatrix} 0 \\ 1 \\ -1 \end{pmatrix}$ of matrix $A$. Based on this information, answer the given sub-questions. Find the value of *α* + 2*β*. Let $A = \begin{pmatrix} 2 & 1 & 1 \\ a & 3 & 2 \\ 3 & b & c \end{pmatrix}$ be a $3 \times 3$ matrix. Let $\alpha$ be the eigenvalue corresponding to the eigenvector $v_1 = \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix}$ and $\beta$ is the eigenvalue corresponding to the eigenvector $v_2 = \begin{pmatrix} 0 \\ 1 \\ -1 \end{pmatrix}$ of matrix $A$. Based on this information, answer the given sub-questions. Which of the following options is/are true ? Figure from the passage in the original paper Which of the following options is/are true?