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(Solved) Let T: R^3 \rightarrow R^3 be the linear transformation given by multiplication by

Question: Let $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ be the linear transformation given by multiplication by

\[A=\left(\begin{array}{ccc} 3 & 1 & -1 \\ -4 & -2 & -4 \\ -5 & -5 & -1 \end{array}\right)\]

Note that 2 is an eigenvalue of this matrix, so that $\lambda-2$ is a factor of the characteristic polynomial of $A$. Find a basis $\mathcal{B}$ for $\mathbb{R}^{3}$ for which the matrix of $T$ with respect to $\mathcal{B}$ is diagonal.

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(Solved) Let T: R^3 \rightarrow R^3 be the linear transformation given by multiplication by

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