Suppose A is a 7x5 matrix. How many pivot columns must A

Last updated: 8/9/2022

Suppose A is a 7x5 matrix. How many pivot columns must A have if its columns are linearly independent? Why? Select the correct answer below. A) The matrix must have ___ pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. B) The matrix must have ___ pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would be linearly dependent. C) The matrix must have ____ pivot columns. The statements "A has a pivot position in every row" and "the columns of A are linearly independent" are logically equivalent. D) None of the columns of A are pivot columns. Any column of A that is a pivot column is linearly dependent with the other pivot columns.