(Solved): Solve the equation for \( X \), given that \( A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\r ...

Solve the equation for \( X \), given that \( A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right] \) and \( B=\left[\begin{array}{rr}0 & 0 \\ 1 & -1\end{array}\right] \). \( 2 X=A-2 B \) \[ x=[\quad] \] Write \( B \) as a linear combination of the other matrices, if possible. (If not, enter DNE in all blanks.) \[ \begin{aligned} B &=\left[\begin{array}{rr} 2 & -1 \\ -3 & 2 \end{array}\right], \quad A_{1}=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right], \quad A_{2}=\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right], \quad A_{3}=\left[\begin{array}{rr} 1 & -1 \\ 1 & 1 \end{array}\right] \\ {\left[\begin{array}{rr} 2 & -1 \\ -3 & 2 \end{array}\right]=\left(\begin{array}{c} \boldsymbol{x} \end{array}\right]\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]+\left(\begin{array}{c} \boldsymbol{x} \end{array}\right]\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right]+(} & \end{aligned} \]