I need answers for questions B, C, D and E. (not hints) And show how you solved them
III Problem 3
Linear Map in the Number Space IR3
Let e = (e1,e2,e3) denote the standard basis of R3. A linear map f : R3 > R3 is given by f(e1)=(1,3,-1),f(e2)=(-2,-2,2) and f(e3)=(3,3,-3)
a) State the mapping matrix of f with respect to basis e .
b) Determine a basis for the kernel of f , and state the dimension of the image space f(R3).
c) We are given the vectors a1 =(2,-2,-1), a2 = (-1,2,1) and a3 = (2,--3,--2) Justify that the set a = (a1, a2, a3) is a basis of R3.
d) State the mapping matrix of f with respect to basis a.
e) Determine three vectors in R3 whose image vectors from f are given by the coor- dinate vector (0,2,0) with respect to basis a .
