題組內容

5. Given $\vec{a}1 = (1, 4, 3)^T$, $\vec{a}2 = (-1, -2, 0)^T$, $\vec{a}3 = (0, 0, 1)^T$, $\vec{a}4 = (2, 2, 3)^T$.

(d)(5%) Let \( \lambda_1, \lambda_2, \cdots, \lambda_n \) be the eigenvalues of matrix A. Prove that \( \det(A) = \lambda_1 \cdot \lambda_2 \cdot \cdots \lambda_n \).