Eigenvectors and linear independence

#linear_algebra

Suppose $T : R^{n} \to R^{n}$ is a linear transformation with distinct eigenvalues $λ_{1}, λ_{2}, \dots, λ_{m}$ , and let $v_{1}, v_{2}, \dots, v_{m}$ be corresponding eigenvectors. Prove $v_{1}, v_{2}, \dots, v_{m}$ are linearly independent.

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Suppose $T:{\bf R}^n\to {\bf R}^n$ is a linear transformation with distinct eigenvalues $\lambda_1, \lambda_2,\ldots, \lambda_m$, and let ${\bf v}_1,{\bf v}_2,\ldots, {\bf v}_m$ be corresponding eigenvectors. Prove ${\bf v}_1,{\bf v}_2,\ldots, {\bf v}_m$ are linearly independent.