Question

Let W=span(v1...vn) and A=(v1...vn) where v1....vn are column vectors of A. Considering the three different row operations, I need to show that applying these changes to the column space gives a set of vectors that spans the same subspace(W).

Any help would be appreciated!

Answer 1

This question doesn't seem very well posed. Row reduce the matrix A to echelon form. The position of the column/s which contain pivot/s are the columns forming the column space. (If there are pivots in col 1, 4, and 7 -- then that means columns 1, 4, and 7 of the NON row reduced matrix form the basis of the colspace.)