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. OA. 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. OB. 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 the form [0 0 0 0 0 0 0 0 1]. so the system is consistent. OC. 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. OD. 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 [000000001]. so the system is inconsistent.
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. OA. 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. OB. 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 the form [0 0 0 0 0 0 0 0 1]. so the system is consistent. OC. 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. OD. 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 [000000001]. so the system is inconsistent.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.
A. 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 [₁ 0 0 0 0 1
1] so the system is consistent.
OB. 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 the form [ 0 0 0 0 0 0 0 0 1]. so the system is consistent.
OC. 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 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 nine columns, must have a row of the form
[000000001]. so the system is inconsistent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1dbff557-c987-45fc-8dd6-6084416c9157%2F0d6daace-d021-4f7e-97d9-f689cfeacdf7%2Fqrvk1xt_processed.jpeg&w=3840&q=75)
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.
A. 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 [₁ 0 0 0 0 1
1] so the system is consistent.
OB. 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 the form [ 0 0 0 0 0 0 0 0 1]. so the system is consistent.
OC. 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 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 nine columns, must have a row of the form
[000000001]. so the system is inconsistent.
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