Question

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}.

Answer 1

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

Answer 2

@SithsAndGiggles yes

Answer 3

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 \(-3c-2d=0\).

Answer 4

ty