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\text { Is } S=\left(\left[\begin{array}{rr} 4 & -5 \\ -6 & 13 \end{array}\right],\left[\begin{array}{rr} -12 & 9 \\ -18 & -3 \end{array}\right],\left[\begin{array}{cc} \frac{3}{2} & 1 \\ -5 & 9 \end{array}\right] \cdot\left[\begin{array}{cc}

\frac{1}{2} & \frac{2}{3} \\ \frac{1}{3} & 1 \end{array}\right]\right) \text { a basis for } M_{22} \text { ? Explain. }

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