Suppose a 4x8 coefficient matrix for a system has four pivot columns. Is the system consistent? Why or why not? Choose the correct answer below. O 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 nine columns, must have a row of the form 0 0 0 0 0 0 0 0 1. so the system is inconsistent. 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 nine columns, could have a row of the form 0 0 0 0 0 0 0 0 1 , so the system could be inconsistent. O C. 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 |, so the system is consistent. O D. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have nine columns and will not have row of the form 0 0 0 0 0 0 0 0 1 , so the system is consistent.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 4CC
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Suppose a 4x8 coefficient matrix for a system has four pivot columns. Is the system consistent? Why or why not?
Choose the correct answer below.
O 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 nine columns, must
have a row of the form 0 0 0 0 0 0 0 0 1.
so the system is inconsistent.
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 nine columns,
could have a row of the form 0 0 0 0 0 0 0 0 1 , so the system could be inconsistent.
O C. 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 |, so the system is consistent.
O D. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have nine columns and will not have
row of the form
0 0 0 0 0 0 0 0 1 , so the system is consistent.
Transcribed Image Text:Suppose a 4x8 coefficient matrix for a system has four pivot columns. Is the system consistent? Why or why not? Choose the correct answer below. O 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 nine columns, must have a row of the form 0 0 0 0 0 0 0 0 1. so the system is inconsistent. 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 nine columns, could have a row of the form 0 0 0 0 0 0 0 0 1 , so the system could be inconsistent. O C. 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 |, so the system is consistent. O D. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have nine columns and will not have row of the form 0 0 0 0 0 0 0 0 1 , so the system is consistent.
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