# Gram - Schmidt Orthogonalization

#### Silver

I have been trying to do this question and I keep getting $$\displaystyle v_3$$ different to what my lecturer has in the notes. Can anyone please find $$\displaystyle v_1$$, $$\displaystyle v_2$$ and $$\displaystyle v_3$$ for me?!

The question is:

Apply the Gram-Schmidt orthogonalization procedure to the R-basis $$\displaystyle \{{1, x, x^2, x^3}\}$$ to obtain an orthonormal basis for $$\displaystyle P_3(R)$$ where the inner product is defined by

$$\displaystyle \int_{-1}^{1} (1-x^2)f(x)g(x) \, dx$$​
The equations used in the process are here

I dont need the working out, I just want to know the final answers for $$\displaystyle v_1$$, $$\displaystyle v_2$$ and $$\displaystyle v_3$$. Thank you!

#### tonio

I have been trying to do this question and I keep getting $$\displaystyle v_3$$ different to what my lecturer has in the notes. Can anyone please find $$\displaystyle v_1$$, $$\displaystyle v_2$$ and $$\displaystyle v_3$$ for me?!

The question is:

The equations used in the process are here

I dont need the working out, I just want to know the final answers for $$\displaystyle v_1$$, $$\displaystyle v_2$$ and $$\displaystyle v_3$$. Thank you!

Instead of doing all the lengthy GM process tell us what's what you get and what's what your lecturer gets: this stuff is fairly simple to check, because the result must be orthonormal...(Wink)
That way we can decide who's wrong ,where and why.

Tonio

#### Silver

I actually got it now, sorry about that
I didnt cancel something at some point and it gave me totally different answer! I just had to be more careful! Thank you anyways!