(Solved): Let \( V \) be the vector space of symmetric \( 2 \times 2 \) matrices and \( W \) be the subspace ...

Let \( V \) be the vector space of symmetric \( 2 \times 2 \) matrices and \( W \) be the subspace \[ W=\operatorname{span}\left\{\left[\begin{array}{cc} -3 & -5 \\ -5 & 2 \end{array}\right],\left[\begin{array}{cc} -3 & -2 \\ -2 & 4 \end{array}\right]\right\} . \] a. Find a nonzero element \( X \) in \( W \). \[ X=\left[\begin{array}{l} \square \\ \end{array}\right] \] b. Find an element \( Y \) in \( V \) that is not in \( W \). \[ Y=\left[\begin{array}{l} 2 \\ \end{array}\right] \]