Help with eigenvalues from matrix

[Sparky_]

Homework Statement

find the eignevalues (a part of a larger problem) for

A= | -4 1 1 |
| 1 5 -1 |
| 0 1 -3 |

Homework Equations

The Attempt at a Solution

= | -4-x 1 1 |
| 1 5-x -1 |
| 0 1 -3-x |

(-4-x)[ (5-x)(-3-x) + 1 ] - (1)[ (1)(-3-x) - 0] + (1)[1-0]

(-4-x)[ x^2 -2x -14] + x + 4

(-4)[-x^3 + 2x^2 + 14x] + x + 4

4x^3 - 8x^2 - 56x + x + 4

4x^3 - 8x^2 - 55x + 4

I do not see the roots for the above being -3, -4, and 5.


The book has x1 = -3, x2 = -4, and x3 = 5.

When I run the eigenvalue routine in the software package Maxima, I believe I am getting (-3 -4,5) - output is a little confusing. - anyway I am seeing the same numbers

When I expand (x+3)(x+4)(x-5)

I get 3x^3 - 3x^2 - 60x.

Help?

Thanks
Sparky_

 

[gb7nash]

(-4-x)[ (5-x)(-3-x) + 1 ] - (1)[ (1)(-3-x) - 0] + (1)[1-0]

(-4-x)[ x^2 -2x -14] + x + 4

(-4)[-x^3 + 2x^2 + 14x] + x + 4

Found it. You're not properly multiplying (-4-x) by [ x^2 -2x -14]. Unfortunately, you can't just multiply by the -x and then by -4 (I wish you could). Instead:

(-4-x)[ x^2 -2x -14] = (-4)[ x^2 -2x -14] - x[ x^2 -2x -14] = ...

 

[Sparky_]

Crap - (embarrassed)

it's been too long since I've done this - out of practice

Thanks for the help!