Question: Explain why \[S=\left\{ \left[ \begin{matrix} 1 & 0 \\ 0 & 0 \\ \end{matrix} \right],\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right],\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right],\left[ \begin{matrix} 7 & 4 \\ 4 & 3 \\ \end{matrix} \right] \right\}\] not a basis for is \[{{M}_{2,2}}.\]

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