Question

A = [4,0,1
-1,-6-2
5, 0, 0]

Could somebody please explain how to find the eigenvalues showing all working. I keep getting lost during expanding. Thanks

Answer 1

write out the charateristic polynomial: det(A-lamda I )
= det ()\[\det(\left[\begin{matrix}4-\lambda & 0 & 1 \\ -1 & -6-\lambda&-2\\ 5 &0 & -\lambda \end{matrix}\right]) = (4-\lambda)(-6-\lambda)( -\lambda) + 5(6+\lambda)\]
\[= -\lambda^3-2\lambda^2+29\lambda +30 \]
solve for lamda when this expresstion =0 that is
\[ -\lambda^3-2\lambda^2+29\lambda +30 =0 \] the solutions are eigenvalues

Answer 2

Wip thanks bra, could you show me the step to obtain the eigenvalues

Answer 3

I dont know if there's an easier way, but using the root formular of cubic func, lamda= 5, -1 or -6 so there are three eigvalues

Answer 4

-b+or-sqrt b^2 * 4ac/2a is this what you used?

Answer 5

nope that's for quadratic eqn, the formula for cubic eqn is much more crazy..
or you can use http://www.wolframalpha.com to solve it ...

Answer 6

ok thanks for your help