sidebar interaction. Press tab to begin. Let S= \{ A \in \mathbb{R}^{2 \times 2} \text{ s.t. } \text{trace}(A)=0 \}. Find the representation vector of the matrix A=\begin{bmatrix} 2 & 5 \\ -3 & -2 \end{bmatrix} with respect to the standard basis of S: \left\{ \begin{bmatrix}1 & 0 \\ 0 & -1 \end{bmatrix}, \begin{bmatrix}0 & 1 \\ 0 & 0 \end{bmatrix}, \begin{bmatrix}0 & 0 \\ 1 & 0 \end{bmatrix} ight\} Hint: Follow the same procedure as in the video for determining the representation vectors for B_1, B_2 and B_3, i.e. determine coefficients x_1 , x_2 and x_3 such that \begin{bmatrix} 2 & 5 \\ -3 & -2\end{bmatrix} = x_1 \begin{bmatrix}1 & 0 \\ 0 & -1 \end{bmatrix} +x_2 \begin{bmatrix}0 & 1 \\ 0 & 0 \end{bmatrix}+x_3 \begin{bmatrix}0 & 0 \\ 1 & 0 \end{bmatrix}