Prove by writing out all the terms the validity of the follo

Prove, by writing out all the terms, the validity of the following p(A^alpha e_alpha) = A^alpha p(e_alpha). Let the components of p be (-1, 1, 2, 0), those of A be (2, 1, 0, -1) and those of B be (0, 2, 0, 0). Find p(A); ) p(B) p(A - 3B); p(A) - 3p(B).

Solution

p=(-1,1,2,0)

A=(2,1,0,-1)

pA=-2+1+0+0=-1

AP=-2+1+0+0=-1

pA=Ap

(ii)pB=0+2+0+0=2

(3)p(A-3B)=p(2,-5,0,-1)=-2-5+0+0=-7