$1.00 Find the eigenvales and eigenvectos of the following martix.
- This tutorial hasn't been purchased yet.
- Posted on Mar 19, 2009 at 6:29:20PM
A:
Preview: ... lt if you want to know how to find them. <br>The eigen vectors are <br>V =<br><br> -0.5695 ...
The full tutorial is about 133 words long .
$5.00 Full solution with every single step included
- This tutorial hasn't been purchased yet.
- Posted on Mar 19, 2009 at 7:09:04PM
A:
Preview: ... mn 3, let v3=t.<br>Then v1 = 3t/4, and v2 = -7t/4<br>So v=(v1,v2,v3) =(3t/4,-7t/4,t)<br>=t(3/4,-7/4,1)<br>So the eigenvectors associated to x=0 are:<br>span(3/4,-7/4,1)<br><br>Eigenvectors for other 2 eigenvalues<br>------------------------------------<br>In this row reduction, I will leave x as just x, and substitute at the end.<br>A - xI<br>= <br>-x 4 7<br>1 5-x 8<br>2 2 2-x<br><br>Row reducing:<br>Swap Row 1 and Row 2:<br>1 5-x 8<br>-x 4 7<br>2 2 2-x<br><br>Row2 --> Row2 + xRow1<br>Row3 --> Row3 - 2Row1<br><br>1 5-x 8<br>0 4+5x-x^2 7+8x<br>0 -8+2x -14-x<br><br>Swap Row 3 and Row 2:<br>1 5-x 8<br>0 -8+2x -14-x<br>0 4+5x-x^2 7+8x<br><br>Row 1-> (-8+2x)Row1 - (5-x)Row2<br>Row 3-> (-8+2x)Row3 - (4+5x-x^2)Row2<br>-8+2x 0 6+7x-x^2<br>0 -8+2x -14-x<br>0 0 -x^3+7x^2+24x<br><br>Notice that the bottom right entry is the characteristic polynomial. Since we know that our eigenvalue x is a root of that polynomial, it evaluates to 0:<br><br>2x-8 0 6+7x ...
The full tutorial is about 631 words long .
