I dont know what P2 is, but I am guessing these are polynomials. is just evaluating at 0 which always leaves the constant term of a polynomial. 4 fails for many reasons, for one, if then but is not the 0 polynomial.
Please help me in these problems
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