## anonymous 4 years ago f(x)=Ax +b g(x)=Cx +d, where A and C are 2x2 matrix and b and d are a column vector and x is a column vector (x y) What is f(g(x))?

1. anonymous

$f(x)=\left[\begin{matrix}4 & 5 \\ 2 & 3\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right) +\left(\begin{matrix}1 \\ 1\end{matrix}\right)$and $g(x)=\left[\begin{matrix}2 & 4 \\ 3 & 1\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right)+\left(\begin{matrix}0 \\ 6\end{matrix}\right)$ What is$f(g(x))$?

2. phi

f(g(x))= A(Cx+d)+b = ACx + Ad +b $Ad= \left[\begin{matrix}4 & 5\\ 2 & 3\end{matrix}\right]\left(\begin{matrix}0 \\ 6\end{matrix}\right)=\left(\begin{matrix}30 \\ 18\end{matrix}\right)$ add in b to get $\left(\begin{matrix}31 \\ 19\end{matrix}\right)$ you can figure out AC, right?

3. anonymous

Thanks a bunch phi.