1.Let A be an m*n matrix in reduced row echelon form, and let 1 <=i <= n. Assume that any solution of Ax= 0 has xi= 0. Explain why the ith column of A is a pivot column.
2.Describe an algorithm whose input is a matrix, and whose output is its reduced row echelon form. (Describe the algorithm in plain English. Note that the existence of such an algorithm implies that any matrix can be put in reduced row echelon form after a sequence of row operations.)