4. (10 points) Let $\lambda_1, \lambda_2, \dots, \lambda_n$ be a complete set of eigenvalues of the matrix $A \in \Re^{n \times n}$. Prove that

a. $det(A) = \lambda_1\lambda_2\dots \lambda_n$

阿摩線上測驗 · 2026-10-22T13:47:20+08:00

4. (10 points) Let λ_1, λ_2, , λ_n be a complete set of eigenvalues of the matrix A ^n × n. Prove that a. det(A) = λ_1λ_2 λ_n

4. (10 points) Let $\lambda_1, \lambda_2, \dots, \lambda_n$ be a complete set of eigenvalues of the matrix $A \in \Re^{n \times n}$. Prove that

a. \(det(A) = \lambda_1\lambda_2\dots \lambda_n\)