Im preparing for a linear algebra exam and im trying to solve the next exercise:
We are given a matrix A:
7 −4 0 a −7 b 3 −2 0
which eigenvalues are −1 and 1.Find the parameters a, b∈R.
I honestly have no idea how to solve this but it seems like it should be easy. I know how to find eigenvalues given a matrix. It is done by finding the characteristic polynomial.
And the eigenvectors can be found by solving the system:
7x-4y = lambx ax-7y+b = lamby 3x-2y = lambz
If i am correct,i can assign a value to x and solve for y and z. It feels like im missing something obvious.