3. The purpose of this question is to describe a method of completing a given independent set to a basis and to prove its validity. Let 01,... VK F" be linearly independent. . Let A be the kx n matrix whose th row is vi. Let A be an echelon form of A obtained by applying row-operations. Let i1,j2,..., jm be the indices of the columns of Ae that do not have pivots. Prove that (v1,02,..., Vk, lipoliz...,eim) is a basis for F", where (21,22,...,en} is the stan- dard ordered basis for FN. 3. The purpose of this question is to describe a method of completing a given independent set to a basis and to prove its validity. Let 01,... VK F" be linearly independent. . Let A be the kx n matrix whose th row is vi. Let A be an echelon form of A obtained by applying row-operations. Let i1,j2,..., jm be the indices of the columns of Ae that do not have pivots. Prove that (v1,02,..., Vk, lipoliz...,eim) is a basis for F", where (21,22,...,en} is the stan- dard ordered basis for FN