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

The matrix is:

|1 2|

|3 4|

**3. The attempt at a solution**

I've worked out the eigenvalues to be [tex]\stackrel{\underline{5\pm\sqrt{33}}}{2}[/tex]

But when I plug the first eigenvalue back in I get:

|1 - [tex]\stackrel{\underline{5+\sqrt{33}}}{2}[/tex]........................2 |

|3........................4 - [tex]\stackrel{\underline{5+\sqrt{33}}}{2}[/tex] |

Multiplied by (x,y) = (0,0)

[Sorry I couldn't fit that on the same line as the matrix.]

Which in turn gives two equations:

x*(1-[tex]\stackrel{\underline{5+\sqrt{33}}}{2}[/tex]) + 2y = 0

and

3x + y*(4-[tex]\stackrel{\underline{5+\sqrt{33}}}{2}[/tex]) = 0

Which I can't work out how to solve for the eigenvector.

Is the only solution x=y=0?