(Solved): Let P_(2) be the vector space of all real polynomials of degree at most 2 , i.e., P_(2)={p(t)=a_(0)+ ...

Let P_(2) be the vector space of all real polynomials of degree at most 2 , i.e., P_(2)={p(t)=a_(0)+a_(1)t+a_(2)t^(2):a_(0),a_(1),a_(2) are real numbers. } Define T:P_(2)->R^(2) by T(p)=[[p(0)],[p(1)]]. For instance, if p(t)=1+2t+3t^(2), then T(p)=[[1],[6]]. (a) Show that T is a linear transformation. (b) Find a polynomial p in P_(2) that is in the kernel of T.