Suppose a 5 × 8 coefficient matrix for a system has five pivot columns. Is the s

Question

Suppose a 5 × 8 coefficient matrix for a system has five pivot columns. Is the system consistent? Why or why not? Choose the correct answer below A. 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 O 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 O C. There is a pivot position in each row of the coefficient matrix. The augmented matrix vill have six columns and will not have a row of the D. *There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which wil have the form 0 000 0 o 0 0so the system is consistent. nine columns, could have a row of the form 0 0 o o o 0 0 0 1so the system could be inconsistent. form 0 0 0 0 0 1 so the system is consistent. nine columns, must have a row of the form 0 0 0 0 0 00 0 1 so the system is inconsistent

Explanation / Answer

The option is A). 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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