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## Homework Statement

find closest function a+bx

^{3}to x

^{2}on the iterval [-1,1]

(we consider standard inner product (f,g) = integral(-1 to 1):fgdx

So, here is my attempt, but I got a suspicious result:

[(1,1) (1,x

^{3})] [a]

[(1,x

^{3}) (x

^{3},x

^{3})]

=

[(1,x

[x

then after I've done all the integration I came up with this:

[2 0] [a]

[0 2/7]

=

[(1,x

^{2})][x

^{3}, x^{2})]then after I've done all the integration I came up with this:

[2 0] [a]

[0 2/7]

=

[1/3]

[0]

which means that x=

[1/3]

[0]

which means that x

^{3}term disappears....