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**[SOLVED] Prove A is Diagonalizable (Actual Question)**

**1. Homework Statement**

Suppose that A [tex]\in[/tex] M[tex]^{nxn}[/tex](F) and has two distinct eigenvalues, [tex]\lambda[/tex][tex]_{1}[/tex] and [tex]\lambda[/tex][tex]_{2}[/tex], and that dim(E(subscript [tex]\lambda[/tex][tex]_{1}[/tex] ))= n-1. Prove that A is diagonalizable.

**3. The Attempt at a Solution**

So far, I know that dim(E subscript [tex]\lambda[/tex]2) [tex] \geq1[/tex]

and that

dim(E subscript [tex]\lambda[/tex]1) + dim(E subscript [tex]\lambda[/tex]2) [tex] \leq[/tex] n.

So dim(E subscript [tex]\lambda[/tex]2) = 1.

I am not exactly sure how this helps me to show A is digonalizable. Maybe I am thinking of something else and don't need this to prove A is diagonalizable. Please help.

(Also, sorry about my prevous blank post; I am new)