## anonymous one year ago Consider the ordered bases B = {6−7x,1−x} and C = {2x−3,−(2+4x)} for the vector space P_2. Find the transition matrix from C to the standard ordered basis E = {1,x}.

1. anonymous

So you want to find the 2x2 matrix $$M$$ such that $$CM=E$$, right?

2. anonymous

@SithsAndGiggles yes

3. anonymous

Actually I think it should be $$MC=E$$. $\begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}2x-3\\-2-4x\end{pmatrix}=\begin{pmatrix}1\\x\end{pmatrix}\implies \begin{cases}a(2x-3)-b(2+4x)=1\\ c(2x-3)-d(2-4x)=x\end{cases}$ From the first equation, you find that $$2a-4b=0$$ and $$-3a-2b=1$$. From the second, $$2c+4d=1$$ and $$-3c-2d=0$$.

4. anonymous

ty