Question: Suppose A is a 7x5 matrix. How many pivot columns must A have if its columns are linearly independent? Why? Select the correct answer

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

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. OB. 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. OC. 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. OD. 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.

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