# Linear algebra help

1. Feb 15, 2014

### GregoryGr

1. The problem statement, all variables and given/known data

Calculate the eigenvalues and eigenvectors of the matrix:
$$A= \begin{bmatrix} 3 & 2 & 2 &-4 \\ 2 & 3 & 2 &-1 \\ 1 & 1 & 2 &-1 \\ 2 & 2 & 2 &-1 \end{bmatrix}$$

2. Relevant equations

nothing

3. The attempt at a solution

I've found the eigenvalues, but what disturbes me, is that I can't find a way to make the determinant triangular, as to find the values faster. Can anybody see a way to do that?

2. Feb 15, 2014

### Simon Bridge

You wouldn't make the determinant triangular, the determinant is just one number.

You can make the matrix triangular by row-reduction:
- number the rows top to bottom 1-4.
- reorder the rows: 3-2-4-1 --> 1-2-3-4
- after that the row-reduction to upper-triangular form should come easily.

You probably want to do this for each eigenvalue to find the eigenvectors - so the best order for the rows will be different each time.

You want to try this for the eigenvectors - consider:
http://www.millersville.edu/~bikenaga/linear-algebra/eigenvalue/eigenvalue.html

Last edited: Feb 15, 2014