(a) Use the concept of matrix Rank to argue, without performing ANY calculation, why the columns of this matrix canNOT be linerly independent.

(b) Use Gauss-Jordan elimination method (you can use ReducedRowEchelonForm command) to identify a set B of linearly independent column vectors of A that span the column space of A. Express the column vectors of A that are not included in the set B as a linear combination of the vectors in the set B.

(c) Do the columns of matrix A span the entire Euclidean space "real^3" ? Explain why yes or why not.

A:=<<0,-1,1>|<4,0,-2>|<2,-1,0>|<2,1,1>>;
Matrix(3, 4, [[0, 4, 2, 2], [-1, 0, -1, 1], [1, -2, 0, 1]])