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We have L : P -> R^2

L is a linear transformation with :

[tex]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}[/tex]

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 , x

^{2})of P in the B basis

3/ find matrix L in the canonical basis of P and R^2