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Homework Statement
The linear operator T on R2 has the matrix
<br /> <br /> \begin{bmatrix}4&-5\\-4&-3 \end{bmatrix} <br /> <br /> relative to the basis {(1,2), (0,1)}
Find the eigenvalues of T, and obtain an eigenvector corresponding to each eigenvalue.
Homework Equations
The Attempt at a Solution
So I solved the eigenvalues to be <br /> \lambda = 8, \lambda = -1<br />
I know I normally just sub in the lambda to the matrix and then solve for the null space to get the eigenvector, but how do I do it with a different basis?