- #1
The thinker
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Homework Statement
The matrix is:
|1 2|
|3 4|
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
and3x + y*(4-[tex]\stackrel{\underline{5+\sqrt{33}}}{2}[/tex]) = 0Which I can't work out how to solve for the eigenvector.
Is the only solution x=y=0?