A condition ensuring diagonalizability

#linear_algebra

Suppose $F$ is a field and $A$ is an $n \times n$ matrix over $F$ . Suppose further that $A$ possesses distinct eigenvalues $λ_{1}$ and $λ_{2}$ with $\dim Null (A - λ_{1} I_{n}) = n - 1$ . Prove $A$ is diagonalizable.

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Suppose $F$ is a field and $A$ is an $n\times n$ matrix over $F$. Suppose further that $A$ possesses distinct eigenvalues $\lambda_1$ and $\lambda_2$ with $\dim \operatorname{Null}(A-\lambda_1 I_n)=n-1$. Prove $A$ is diagonalizable.