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 \(\mathbf{v}_{1}, \ldots, \mathbf{v}_{n}\).