Choose the correct answer below. There is at least one row of the coefficient ma

Question

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 nine columns, must have a row of the form [00000000 1 ], so the system is inconsistent. 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 nine columns, could have a row of the form [000000001 ]. so the system could be inconsistent. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have nine columns and will not have a row of the form [0 0 0 0 0 0 0 0 1], so the system is consistent. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have seven columns and will not have a row of the form [00 0 0 0 0 1 ], so the system is consistent.

Explanation / Answer

The answer is C. There is a pivot position in each row of the coefficient matrix. It implies that the augmented matrix , having 9 columns has no row of the form ( 0, 0, 0, 0, 0, 0, 0, 0, 1) so the system is consistent.

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