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find the polynomial in P2 whose coordinate matrix with respect to the basis
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is|dw:1349421000654:dw|
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\[B=\left\{ x+x ^{2} ,1+x\right\}\] this is the basis
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is it gonna be B=(0,0,0) ;(0,1,1);(0,1,0)
|dw:1349421351446:dw|
|dw:1349421421254:dw|
Coolsector
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we need a matrix to make the change between the two basis
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how to find that matrix
Coolsector
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well i have some problem here .. how can B be a basis for some R3 if it has only two vectors
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i think the firt vector is zero
Coolsector
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it's given ?
Coolsector
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but still i dont think it is a basis in this case
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no
Coolsector
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i might dont understand the question but B isnt a basis for P2
Coolsector
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we cant generate for example "1" which is a valid P2
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yes it is
Coolsector
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how come ?
Coolsector
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here i just showed you that it doesnt span P2
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we have been told
Coolsector
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so i dont know .. i dont understand
im sorry
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ok in general how to anser this kind of questions
Coolsector
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you have to find a matrix that converts between the two basis and then you only have to multiply
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eg like wat i did
Coolsector
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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
Coolsector
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im sorry i couldnt help more but i really dont know how
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ok thnx
SWAG
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hmm
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@Coolsector i din't find the answer ,bul i'll try consult to my lecture