Let $V$ be the vector space of symmetric $2\times 2$ matrices and $W$ be the subspace $$W=\text{span} \lbrace \left[\begin{array}{cc} -3 &1\cr 1 &-3 \end{array}\right],\left[\begin{array}{cc} 3 &5\cr 5 &0 \end{array}\right] \rbrace .$$ a. Find a nonzero element $X$ in $W$.
$X =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$

b. Find an element $Y$ in $V$ that is not in $W$.
$Y =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$