Considering the endomorphism $f$ of $R^3$ of
\begin{bmatrix} -3 & 5 & -5\\ -4 & 6 & -5\\ -4& 4 &-3 \end{bmatrix}
relatively of the canonical base bc of $R^3$ find the set S of reals $λ$ such as $rg($M-$λ$I3)<3
What method should I use? I tried the Gaussian elimination but it becomes awkward and difficult at some point. Can you give some details?
Assuming rg means rank, you know that $rg(M-\lambda I_3)\leq 3$. Find the set A of $\lambda$'s for which the rank is 3 (think about when is the rank of a matrix equal to its dimension) and the answer will be $S=\mathbb{R}-A$.