Teaching UP TGT Mock Test Series 2025 Mathematical Science Linear Algebra Matrix Representation of Linear Transformations
Let \( \rm A=\begin{bmatrix}2&3\\\ 4&-1\end{bmatrix}\) then the matrix B that represents the linear operator A relative to the basis \(\rm S=\{u_1, u_2\}=\left\{[1,3]^T,[2,5]^T\right\}\), is:
1
\( \rm A=\begin{bmatrix}53&89\\\ 32&54\end{bmatrix}\)
2
\( \rm A=\begin{bmatrix}-53&-89\\\ 32&54\end{bmatrix}\)
3
\( \rm A=\begin{bmatrix}53&55\\\ 98&23\end{bmatrix}\)
4
\( \rm A=\begin{bmatrix}53&-23\\\ 89&45\end{bmatrix}\)