The equivalent polar equation for the given rectangular - coordinate equation. y= -3

The reason ehy the point $(-1,\frac{3\pi }{2})$ lies on the polar graph $r=1+\cos \theta$ even though it does not satisfy the equation.

The coordinates of the point in the \(\displaystyle{x}

Consider the bases $B=\left(\begin{array}{c}\left[\begin{array}{c}2\\ 3\end{array}\right],\left[\begin{array}{c}3\\ 5\end{array}\right]\end{array}\right)of{R}^{2}andC=(\begin{array}{c}\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right]\end{array},\left[\begin{array}{c}0\\ 1\\ 1\end{array}\right])of{R}^3$.
and the linear maps $S\in L(R^2,R^3)andT\in L(R^3,R^2)$ given given (with respect to the standard bases) by $[S{]}_{E,E}=\left[\begin{array}{cc}2& -1\\ 5& -3\\ -3& 2\end{array}\right]and[T{]}_{E,E}=\left[\begin{array}{ccc}1& -1& 1\\ 1& 1& -1\end{array}\right]$ Find each of the following coordinate representations. ${\displaystyle \left(b\right){\left[S\right]}_{E,C}}$
${\displaystyle \left(c\right){\left[S\right]}_{B,C}}$