# Thread: Linear Algebra Help - Question 2!

1. ## Linear Algebra Help - Question 2!

Determine which of the four inner product axioms do not hold. give a specific example in the case.

In P2, define <p(x), q(x)> = p(0)q(0)

axioms:
1) <u, v> = <v,u>
2) <u, v+w> = <u, v> + <u, w>
3) <cu, v> = c<u, v>
4) <u, u> greater than or equal to 0 if and only if u = 0

2. ## P2?

I dont know what P2 is, but I am guessing these are polynomials. $p(0)$ is just evaluating at 0 which always leaves the constant term of a polynomial. 4 fails for many reasons, for one, if $p(x)=x$ then $ = p(0)*p(0)=0*0=0$ but $p(x)=x$ is not the 0 polynomial.