Problem 8. (10 Points) Let A E L(R) Be Linear Mapping Given By Matrix 1 1 E AX 1 2 1 -1 2 1 Where

Problem 8. (10 Points) Let A E L(Rº) Be Linear Mapping Given By Matrix 1 1 E AX 1 2 1 -1 2 1 Where X = ((0,2,0), (1,-1,0), (1,0,1)) Is A Basis Of R3. A) Find Rank, Nullity, And Kernel Of Mapping A. B) Find Matrix X A. C) Find All Vectors R E R3 For Which Ax (-1,1,0).

 

 

Problem 8. (10 points) Let A EL(R) be linear mapping given by matrix 1 1 1 AX -1 2 1 where x = ((0,2,0), (1, 1,0), (1, 0, 1)) is a basis of R. a) Find rank, nullity, and kernel of mapping A. b) Find matrix x A. c) Find all vectors x = R for which Ax = (-1,1,0).