Homework SourseIf a 7 Times 5 augmented matrix has a pivot in every column
Solution
If the augmented matrix of a system of m linear equations in n variables has a pivot in its last column, then the system corresponding to that augmented matrix will be inconsistent. This is because the RREF ( reduced row echelon form ) of the augmented matrix will have a row of the form [00p] where p, the pivot, is a non-zero number. This means that p =0, which is incorrect. This implies that the system of linear equations is inconsistent. Thus, If a 7x5 augmented matrix has a pivot in every column, the corresponding system of equations is inconsistent.
| | If the augmented matrix of a system of m linear equations in n variables has a pivot in its last column, then the system corresponding to that augmented matrix will be inconsistent. This is because the RREF ( reduced row echelon form ) of the augmented matrix will have a row of the form [00p] where p, the pivot, is a non-zero number. This means that p =0, which is incorrect. This implies that the system of linear equations is inconsistent. Thus, If a 7x5 augmented matrix has a pivot in every column, the corresponding system of equations is inconsistent. |
