Suppose a 3x6 coefficient matrix for a system has three pivot columns. Is the system consistent? Why or why not? Choose the correct answer below. A. 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 seven columns, could have a row of the form [Start 1 By 7 Matrix 1st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 6st Column 0 7st Column 1 EndMatrix ], so the system could be inconsistent. B. 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 seven columns, must have a row of the form [Start 1 By 7 Matrix 1st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 6st Column 0 7st Column 1 EndMatrix ], so the system is inconsistent. C. 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 [Start 1 By 7 Matrix 1st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 6st Column 0 7st Column 1 EndMatrix ], so the system is consiste

All the 5 rows of the coefficient matrix (since it is of order 5×8) will have a pivot position. The augmented matrix obtained by adding a last column of constant terms to the 8 columns of the coefficient 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.

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