# Prove Basis for symmetric matrix.

**Let V be the vector subspace of M$_{2}$ ($\mathbb{R})$ consisting of all symmetric matrices, That is A$^{t}$ = A. 1) Show that $\clubsuit$= $\left\{ \left(\begin{array}{cc} 1 & -2\\ -2 & 1 \end{array}\right),\left(\begin{array}{cc} 2 & 1\\ 1 & 3 \end{array}\right),\left(\begin{array}{cc} 4 & -1\\ -1 & -5 \end{array}\right)\right\}$ is a basis for V. 2) Find the co-ordinates of Z = $\left(\begin{array}{cc} 4 & -11\\ -11 & -7 \end{array}\right)$ with respect to this Basis.**

For Part 1) could we argue that the generalised form of a symmetric matrix in M$_{2}$ ($\mathbb{R})$ would be