Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns...

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Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R5? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. O 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 not span R. O C. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R" are logically equivalent. O D. The columns of a 5x7 matrix cannot span R5 because having more columns than rows makes the columns of the matrix dependent. Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R5? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. O 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 not span R. O C. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R" are logically equivalent. O D. The columns of a 5x7 matrix cannot span R5 because having more columns than rows makes the columns of the matrix dependent.