Consider the following pairs of vector spaces V with functions

1. Consider the following pairs of vector spaces V with functions (, ): V X V > R. In each case, either prove that this function is an inner product, or give an example to demonstrate that one of the inner product conditions fails. (a) V = PAIR), the polynomials over R of degree at most 2, and (197(1) = P(0)Q\"(0) + p'(0)tJ'(0) + 10\"(0)q(0)- ( mfg? 3:22:922 ' $1 1172 _ 1'1y1+$192+$2yz- (d) V={(:c,0,z):x,z]R} R3 and $1 $2 311 7 312 = $1582 + 331292 + Z132- Z1 22 (c) V = R2 and