Question

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

Answer 1

Answer:

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Step-by-step explanation:

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.