So I got this problem for homework and was able to finish part a where I need to draw an eigenvector on a level curve but I can't solve part b
I'm assuming I need to separate it into $qA(v_1)-qA(v_2)$, but I don't know how to find the difference without the eigenvector or the matrix $A$. Do I need to use the diagonalization formula? If so, how can I use it in this case?
"Assume that the graph below represents the level curves of the function $qA(x, y)$ for some $2 \times 2$ matrix $A$. Assume moreover that $A$ has eigenvalues $\lambda_1 = −2$ and $\lambda_2 = −3$.
A) On the graph below draw an eigenvector $v_2$ corresponding to the eigenvalue $\lambda_2 = −3$.
B) Let $v_1$ be length $2$ eigenvector of $A$ with corresponding eigenvalue $−2$, and $v_2$ be length $3$ eigenvector of $A$ with corresponding eigenvalue $−3$. Find the value of $qA (v_1-v_2)"$