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.O A. The matrix must havepivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution.O B. The matrix must havepivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would be linearly dependent.O C. The matrix must havepivot columns. The statements "A has a pivot position in every row" and "the columns of A are linearly independent" are logically equivalent.O 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. 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 havepivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution.O B. The matrix must havepivot 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 havepivot columns. The statements "A has a pivot position in every row" and "the columns of A span R5" 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.

Given that A is a 5×7 matrix. There are 5 equations with 7 unknowns. If number of unknowns are…

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. 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 be linearly dependent. O 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. O 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.