define operation in P1 such that for pxa0a1x and qxb0b1x we

define operation * in P1 such that for p(x)=a0+a1x and q(x)=b0+b1x we have p*q=a0b0+a1b1. Determine whether or not * is an inner product for P1. if it is, prove all properties and if it is not, give an example for all properties violated.

Solution

* operation is a Dot/scalar product in vector algebra.

Properties :

A*B = B*A

A*(B+C) = A*B + A*C