Please help with this matrix question! Solve for Eigenvales, and Eigenvectors

  • Thread starter sidinsky
  • Start date
  • #1
6
1
M = (a c)
(c b)

Sorry for the double sets of brackets, its all in one. I'll also show as far as i got below:

[a-λ c] => (a-λ)(b-λ) - c^2 = λ^2 + (-a-b)λ + (ab-c^2) =0
[c b-λ] =>

then using the quadratic formula: λ = [-(-a-b) +/- Sqrt{(-a-b)^2 - 4(1)(ab-c^2)}]/ 2

then after some algebra I got stuck: λ = [(a+b) +/- Sqrt{a^2 + 2ab + b^2 -4ac^2}]/2

λ = [(a+b) +/- Sqrt{a^2 - 2ab + b^2 + c^2}]/2 ==>> THIS IS WHERE I GOT STUCK. PLEASE HELP
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
welcome to pf!

hi sidinsky! welcome to pf! :wink:

(have a square-root: √ and a ± and try using the X2 button just above the Reply box :wink:)
λ = [(a+b) +/- Sqrt{a^2 - 2ab + b^2 + c^2}]/2

looks ok :smile:

that gives you the two eigenvalues,

so now use the standard techniques to find an eigenvector for each :wink:
 
  • #3
6
1
is there any way this expression can be simplified further? I am sorta having trouble with the algebra :S
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
251
is there any way this expression can be simplified further?

i don't think so

how far have you got?​
 
  • #5
6
1
well I managed to clean up the expression inside the sqrt a bit to: [(a-b)2 + c 2 ]/2

a2 -2ab + b2 + c2 = (a-b)2 + c2

λ1 = (a+b) + sqrt{(a-b)2 +c 2}[itex]/2[/itex]

and λ2 = (a+b) - sqrt{(a-b)2 + c2}[itex]/2[/itex]

now these expressions for Lambda are too difficult for me to use to solve for eigenvectors
 

Related Threads on Please help with this matrix question! Solve for Eigenvales, and Eigenvectors

Replies
6
Views
2K
Replies
11
Views
6K
Replies
4
Views
1K
Replies
5
Views
1K
Replies
10
Views
2K
Replies
5
Views
752
Replies
6
Views
11K
Replies
0
Views
1K
Replies
15
Views
6K
Top