Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent. O A. The system is consistent because the rightmost column of the augmented matrix is not a pivot column. O B. The system is consistent because all the columns in the augmented matrix will have a pivot position. OC. The system is consistent because the augmented matrix will contain a row of the form [0... 0 b ] with b nonzero. O D. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix.
Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent. O A. The system is consistent because the rightmost column of the augmented matrix is not a pivot column. O B. The system is consistent because all the columns in the augmented matrix will have a pivot position. OC. The system is consistent because the augmented matrix will contain a row of the form [0... 0 b ] with b nonzero. O D. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 93E
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![Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent.
O A. The system is consistent because the rightmost column of the augmented matrix is not a pivot column.
O B.
The system is consistent because all the columns in the augmented matrix will have a pivot position.
O C.
The system is consistent because the augmented matrix will contain a row of the form [0... 0 b ] with b nonzero.
O D. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1dbff557-c987-45fc-8dd6-6084416c9157%2Fa0e130f8-e9ec-4fcd-8fc5-6d00f69daec4%2Fpxikrwi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent.
O A. The system is consistent because the rightmost column of the augmented matrix is not a pivot column.
O B.
The system is consistent because all the columns in the augmented matrix will have a pivot position.
O C.
The system is consistent because the augmented matrix will contain a row of the form [0... 0 b ] with b nonzero.
O D. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix.
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