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## Homework Statement

The Matrix A is as follows

A= [4 -4 0

2 -2 0

-2 5 3]

and has 3 distinct eigenvalues λ1<λ2<λ3

Let Vi be the unique eigenvector associated with λi with a 1 as its first nonzero component.

Let

D = [ λ1 0 0

0 λ2 0

0 0 λ3]

and P= [v1|v2|v3]

Find D and P.

## Homework Equations

not going to right it out but I know you find eigenvectors by (λI-A)X = 0

and eigenvalues by det(λI-A).

## The Attempt at a Solution

So I already found D with the eigenvalues as {0,2,3}

I tried to solve for P and got

[-1 -2 0

1 1 0

1 1 1]

but this is wrong.

I am kinds confused b/c the textbook says (λI-A)X=0 but my professor uses (A-λI)X=0 in class!