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**linear algebra diagonalization :(**

## Homework Statement

determine whether the given matrix is diagonalizable. where possible, find a matrix

*S*such that

S

^{-1}AS=Diag(λ

_{1}+λ

_{2},...,λ

_{n})

## Homework Equations

## The Attempt at a Solution

I was able to find the eigenvalues, which are λ=1,-4,4. This is given in the back of the book as well, which matched up evenly.

Now, I'm having trouble finding the matrix S. I know I need to find the eigenvectors, and place them as columns in an

*n x n*matrix.

When I plug 1 in, say, I come up with

0 0 0

0 2 7

1 1 -4

And for 4 I came up with

-3 0 0

0 -1 7

1 1 -7

Neither of them seem to be coming out right.

The answer in the back of the book is:

15 0 0

-7 7 1 = S

2 1 -1

Thanks, all.