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
