Question

Is a basis of the space of upper-triangular 2×22×2 matrices. find the coordinates of m=[−8084]m=[−8804] with respect to this basis?

Answer 1

\mathcal{B}=\begin{Bmatrix}\begin{bmatrix} 1 & -2 \\ 0 & 0 \end{bmatrix},\ \begin{bmatrix} 0 & -1 \\ 0 & -3 \end{bmatrix},\ \begin{bmatrix} 0 & 0 \\ 0 & -2 \end{bmatrix} \end{Bmatrix} M=\begin{bmatrix} 0 & 5 \\ 0 & -8 \end{bmatrix},\ \text{find } [M]_\mathcal{B}