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find the polynomial in P2 whose coordinate matrix with respect to the basis

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\[B=\left\{ x+x ^{2} ,1+x\right\}\] this is the basis
is it gonna be B=(0,0,0) ;(0,1,1);(0,1,0) |dw:1349421351446:dw| |dw:1349421421254:dw|

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Other answers:

we need a matrix to make the change between the two basis
how to find that matrix
well i have some problem here .. how can B be a basis for some R3 if it has only two vectors
i think the firt vector is zero
it's given ?
but still i dont think it is a basis in this case
i might dont understand the question but B isnt a basis for P2
we cant generate for example "1" which is a valid P2
yes it is
how come ?
here i just showed you that it doesnt span P2
we have been told
so i dont know .. i dont understand im sorry
ok in general how to anser this kind of questions
you have to find a matrix that converts between the two basis and then you only have to multiply
eg like wat i did
for example moving from S = { (1,2) , (3,5) } basis into the standard R2 basis the matrix is 1 3 2 5 now if you multiply this matrix with S vectors you get them in the standard R2 basis
im sorry i couldnt help more but i really dont know how
ok thnx
@Coolsector i din't find the answer ,bul i'll try consult to my lecture

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