Find eigenvalues of \(A=\begin{bmatrix} 2 & 4\\5 & 3\end{bmatrix}\).
\[\text {Eigenvalues (in increasing order): }\lambda _1=\answer {-2}, \quad \lambda _2=\answer {7}\]

Compute a basis for the eigenspace associated with each of these eigenvalues.

A basis for \(\mathcal {S}_{\lambda _1}\): \(\left \{\begin{bmatrix}1\\\answer {-1}\end{bmatrix}\right \}\)

A basis for \(\mathcal {S}_{\lambda _2}\): \(\left \{\begin{bmatrix}4\\\answer {5}\end{bmatrix}\right \}\)