Determine whether the statement below is true or false. Justify the answer.
If the columns of an mon matrix A span RM, then the equation Axeb is consistent for each bin R m
Choose the correct answer below.
A. This statement is true. Since the columns of A span RM, the augmented matrix [ Ab] has a pivot position in every column.
B. This statement is false. If the columns of A span RM, then the equation Ax = b is inconsistent for each b in IRM m
C. This statement is true. If the columns of A span RM, then the equation Ax = b has a solution for each b in Rm
D. This statement is false. Since the columns of A span RM, the matrix A has a pivot position in exactly m - 1 rows.