# Transfer matrix

#### akimbo

##### New member
Hey i got a problem here but still without correction so if you guys can help me , thanks in advance i'm stuck there

We have L : P -> R^2
L is a linear transformation with :

$$B = \left\{1-x^{2},2x,1+2x+3x^{2} \right\} \; and \; B' = \begin{Bmatrix} \begin{bmatrix} 1\\-1 \end{bmatrix} \begin{bmatrix} 2\\0 \end{bmatrix} \end{Bmatrix} as \; [L]^{B'}_{B} = \begin{bmatrix} 2 &-1 &3 \\ 3&1 & 0 \end{bmatrix}$$

I have to find
1/ the transfer matrix from B' to the canonical basis of R^2
also
2/ the transfer matrix from the canonical basis ( 1 , x , x2 )of P in the B basis
3/ find matrix L in the canonical basis of P and R^2