Suppose a 4 times 7 coefficient matrix for a system has four

Suppose a 4 times 7 coefficient matrix for a system has four pivot columns. Is the system consistent? Why or why not? Choose the correct answer below. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have eight columns, could have a row of the form [ 0 0 0 0 0 0 0 1 1, so the system could be inconsistent. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have eight columns and will not have a row of the form [00000001 1, so the system is consistent. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have five columns and will not have a row of the form [ 0 0 0 0 1 1, so the system is consistent. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have eight columns, must have a row of the form [ 0 0 0 0 0 0 0 1 ], so the system is inconsistent.

Solution

The system must be consistent. Because the matrix is the coefficiente matrix and each row has a pivot, it means for the augmented matrix no row is of the form (0,...,0,b)

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