Show that the linear transformation $R$ is not injective by finding two different elements of the domain, $\vect{x}$ and $\vect{y}$, such that $\lt{R}{\vect{x}}=\lt{R}{\vect{y}}$. ($S_{22}$ is the vector space of symmetric $2\times 2$ matrices.) \begin{equation*} \ltdefn{R}{S_{22}}{P_1}\quad \lt{R}{\begin{bmatrix}a&b\\b&c\end{bmatrix}}=(2a-b+c)+(a+b+2c)x \end{equation*}