Orthonormal, Polynomial ....!

[Deera]

i would like to get help on this question please, open the attached pics, i do not even understand the question it self !?

 

[HallsofIvy]

i would like to get help on this question please, open the attached pics, i do not even understand the question it self !?

One difficulty is that the formula for the projection is wrong. It should be that the "projection of p(x) on q(x)" is given by \(\displaystyle \frac{p(x)\int_0^1 p(y)q(y)dy}{\int_0^1 p^2(z) dz}\) (the denominator is the "inner product of p with itself").

Now, you are asked to put \(\displaystyle p(x)= x\) and \(\displaystyle q(x)= 1\) and do that calculation: \(\displaystyle \frac{x\int_0^1 dy}{\int_0^1 z^2 dz}\)

 

[Deera]

thank you!

that is actually true, the formula is wrong and the TA also says so, and yeah we should use gram schmidt process in order to find the missing value, am i right ?