Prove that if (k=) const and matrix (mathbf{A}) has eigenvalues (lambda_{1}, ldots, lambda_{n}), with corresponding eigenvectors (mathbf{v}_{1},

Question:

Prove that if $k=$ const and matrix $\mathbf{A}$ has eigenvalues $\lambda_{1}, \ldots, \lambda_{n}$, with corresponding eigenvectors $\mathbf{v}_{1}, \ldots, \mathbf{v}_{n}$, then the eigenvalues of $k \mathbf{A}$ are $k \lambda_{1}, \ldots, k \lambda_{n}$, with eigenvectors $\mathbf{v}_{1}, \ldots, \mathbf{v}_{n}$.

Fantastic news! We've Found the answer you've been seeking!