# Explain why S is not a basis for M_{2,2} S=left{begin{bmatrix}1 & 0 0 & 1 end{bmatrix},begin{bmatrix}0 & 11 & 0 end{bmatrix},begin{bmatrix}1 & 1 0 & 0 end{bmatrix}right}

Explain why S is not a basis for ${M}_{2,2}$
$S=\left\{\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],\left[\begin{array}{cc}1& 1\\ 0& 0\end{array}\right]\right\}$
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Willie
Step 1
We have given a set of the matrices
$S=\left\{\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],\left[\begin{array}{cc}1& 1\\ 0& 0\end{array}\right]\right\}$
Step 2
S is said to be a spanning set of V if its linear span is exactly to V.
In the given set of matrices S spans the whole space ${M}_{2,2}$ which is strictly larger than V. So, S not a spanning set of V.
Hence , S is not basis for ${M}_{2,2}$
Jeffrey Jordon