Machine Learning Foundations Quiz 1: 7 July 2024 (May 2024 term)

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 + 2β.

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 ?

Which of the following options is/are true?