Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R^5? Why? a. The matrix must have nothing pivot columns. If A had fewer pivot columns, then the equation A would have only the trivial solution.
b. The matrix must have nothing pivot columns. The statements "A has a pivot position in every row" and "the columns of A span " are logically equivalent.
c. The matrix must have nothing pivot columns. Otherwise, the equation A would have a free variable, in which case the columns of A would not span .
d. The columns of a 57 matrix cannot span because having more columns than rows makes the columns of the matrix dependent