Math / AlgebraQuestionLet T:R2→R2T: R^{2} \rightarrow R^{2}T:R2→R2 be the linear operator defined by T([x1x2])=[5x1−x25x1+x2]T\left(\left[\begin{array}{c} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{c} 5 x_{1}-x_{2} \\ 5 x_{1}+x_{2} \end{array}\right]T([x1x2])=[5x1−x25x1+x2] and let B={u1,u2}B=\left\{\boldsymbol{u}_{1}, \boldsymbol{u}_{2}\right\}B={u1,u2} be the basis for which u1=[15],u2=[−10]\boldsymbol{u}_{1}=\left[\begin{array}{l}1 \\ 5\end{array}\right], \boldsymbol{u}_{2}=\left[\begin{array}{c}-1 \\ 0\end{array}\right]u1=[15],u2=[−10]. Find [T]B[T]_{B}[T]B. [T]B=(□[T]_{B}=(\square[T]B=(□Studdy Solution[T]B=[2−124][T]_B = \begin{bmatrix} 2 & -1 \\ 2 & 4 \end{bmatrix}[T]B=[22−14]View Full Solution - FreeWas this helpful?
