(i) If A is symmetric and det(A) > 0, then A is positive definite.

4. (10%) Let $L$ be a linear operator on $\mathbb{R}^2$, and let $v_1 = \begin{bmatrix} 1 \\ 3 \end{bmatrix}$, $v_2 = \begin{bmatrix} -3 \\ 5 \end{bmatrix}$, $v_3 = \begin{bmatrix} -9 \\ 1 \end{bmatrix}$. (a) Are $\pmb{v}_1, \pmb{v}_2$, and $\pmb{v}_3$ linearly independent?

(i) If A is symmetric and det(A) > 0, then A is positive definite.

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