Originally Posted by

**tn11631** Let W be the subspace of M_2x2 (R) consisting of the symmetric 2x2 matrices. The set

S= {$\displaystyle

\begin{pmatrix}

0 & -1 \\

-1 & 1

\end{pmatrix}$, $\displaystyle

\begin{pmatrix}

1 & 2 \\

2 & 3

\end{pmatrix} $$\displaystyle

\begin{pmatrix}

2 & 1 \\

1 & 9

\end{pmatrix} $

$\displaystyle

\begin{pmatrix}

1 & -2 \\

-2 & 4

\end{pmatrix}$

$\displaystyle

\begin{pmatrix}

-1 & 2 \\

2 & -1

\end{pmatrix} $}

generates W. Find a subset of S that is a basis for W.

(I'm not sure what all the (0)'s are next to my matrices but they aren't supposed to be there its only supposed to be the 5 matrices)