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})

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

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