cool_dude
Feb 15, 2008, 08:16 PM
I know how to compute determinants its not very difficult but I get confused when there are weird notations thrown in. So I'm not exactly sure on this question
computer det(A-λI) for this linear system
x_1 + 2x_2 = λx_1
2x_1 + x_2 = λx_2
I know that the characteristic equation is
λ^2 - 2λ + 1
the eigenvalues are solutions to this equation so they are λ = 1
Anyhow I'm not sure if that little bit was needed. But this is how I think the question should be solved by applying the same principles of solving determinants. You put it into the form (A-λI)x = 0 so you got a matix 2x2 and you do ad-bc so you get the determinant to be λ^2 - 2λ - 3. I'm really not sure about this. Please if somebody can tell me how to do this question easier or even if my answer is correct that would be great. Thanks
computer det(A-λI) for this linear system
x_1 + 2x_2 = λx_1
2x_1 + x_2 = λx_2
I know that the characteristic equation is
λ^2 - 2λ + 1
the eigenvalues are solutions to this equation so they are λ = 1
Anyhow I'm not sure if that little bit was needed. But this is how I think the question should be solved by applying the same principles of solving determinants. You put it into the form (A-λI)x = 0 so you got a matix 2x2 and you do ad-bc so you get the determinant to be λ^2 - 2λ - 3. I'm really not sure about this. Please if somebody can tell me how to do this question easier or even if my answer is correct that would be great. Thanks