# finding a matrix with respect to basis

$$B = \left\{1-x^{2},2x,1+2x+3x^{2} \right\} \; and\; B' = \begin{Bmatrix} \begin{bmatrix} 1\\-1 \end{bmatrix} \begin{bmatrix} 2\\0 \end{bmatrix} \end{Bmatrix} is \; [L]^{B'}_{B} = \begin{bmatrix} 2 &-1 &3 \\ 3&1 & 0 \end{bmatrix}$$ Let L be a linear transformation : $$L : P_{2}\rightarrow R^{2}$$

I have to find the matrix L with respect to the standard basis of $$P_{2}$$ and $$R^{2}$$

i stuck also with the change of basis matrix from the standard basis ( 1 , x , x^2) of $$P_{2}$$ to the basis B

Much appreciated , thanks in advance