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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. O A. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have four columns and will not have a row of the form 0 0 0 1 , so the system is consistent. 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 seven columns, could have a row of the form 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 seven columns and will not have a row of the form 0 0 0 0 0 0 1 , so the system is consistent. O D. 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 [0 00 0 0 0 so the system is inconsistent,

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. O A. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have four columns and will not have a row of the form 0 0 0 1 , so the system is consistent. 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 seven columns, could have a row of the form 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 seven columns and will not have a row of the form 0 0 0 0 0 0 1 , so the system is consistent. O D. 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 [0 00 0 0 0 so the system is inconsistent,

College Algebra
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 3x6 coefficient matrix for a system has three pivot columns. Is the system consistent? Why or why not? Choose the correct answer below. O A. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have four columns and will not have a row of the form [0001]. so the system is consistent. 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 seven columns, could have a row of the form o 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 seven columns and will not have a row of the form 0 0 0 0 0 0 1 , so the system is consistent. O D. 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 0 0 0 0 0 0 1, so the system is inconsistent.
Transcribed Image Text: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. O A. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have four columns and will not have a row of the form [0001]. so the system is consistent. 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 seven columns, could have a row of the form o 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 seven columns and will not have a row of the form 0 0 0 0 0 0 1 , so the system is consistent. O D. 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 0 0 0 0 0 0 1, so the system is inconsistent.
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