# Find the transformation matrix Let B = <mo fence="false" stretchy="false">{ 2 x

Find the transformation matrix
Let $B=\left\{2x,3x+{x}^{2},-1\right\},{B}^{\prime }=\left\{1,1+x,1+x+{x}^{2}\right\}$
Need to find the transformation matrix from $B$ to ${B}^{\prime }$.
I know that:
$\left(a{x}^{2}+bx+c{\right)}_{B}=\left(\frac{b-3c}{2},c,-a\right)$
$\left(a{x}^{2}+bx+c{\right)}_{{B}^{\prime }}=\left(a-b,b-c,c\right)$
How to proceed using this info in order to find the transformation matrix?
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SweallySnicles3
Let ${B}_{c}=\left(1,x,{x}^{2}\right)$ the canonical basis. Let ${P}_{B\to {B}_{c}}$ the transformation matrix from ${B}_{c}$ to $B$ and ${P}_{{B}^{\prime }\to {B}_{c}}$ the transformation matrix from ${B}_{c}$ to ${B}^{\prime }$ then the transformation matrix from $B$ to ${B}^{\prime }$ is
${P}_{{B}^{\prime }\to B}={P}_{{B}^{\prime }\to {B}_{c}}{\left({P}_{B\to {B}_{c}}\right)}^{-1}$