Determine whether the statement below is true or false. Justify the answer. The equation Ax=b is consistent if the augmented matrix [a b] has a pivot position in every row. Choose the correct answer below. C A. This statement is false. The augmented matrix A b than rows. OB. This statement is true. The pivot positions in the augmented matrix [ A b] always occur in the columns that represent A. OC. This statement is true. If the augmented matrix [ A b] has a pivot position in every row, then the equation Ax=b has a solution for each b in R™. cannot have a pivot position in every row because it has more columns D. This statement is false. If the augmented matrix [ A b] has a pivot position in every row, the equation Ax = b may or may not be consistent. One pivot position may be in the column representing b.
Determine whether the statement below is true or false. Justify the answer. The equation Ax=b is consistent if the augmented matrix [a b] has a pivot position in every row. Choose the correct answer below. C A. This statement is false. The augmented matrix A b than rows. OB. This statement is true. The pivot positions in the augmented matrix [ A b] always occur in the columns that represent A. OC. This statement is true. If the augmented matrix [ A b] has a pivot position in every row, then the equation Ax=b has a solution for each b in R™. cannot have a pivot position in every row because it has more columns D. This statement is false. If the augmented matrix [ A b] has a pivot position in every row, the equation Ax = b may or may not be consistent. One pivot position may be in the column representing b.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Determine whether the statement below is true or false. Justify the answer.
The equation Ax=b is consistent if the augmented matrix [a b] has a pivot position in every row.
Choose the correct answer below.
C
A. This statement is false. The augmented matrix A b
than rows.
OB. This statement is true. The pivot positions in the augmented matrix [ A b] always occur in the columns that represent A.
OC. This statement is true. If the augmented matrix [ A b] has a pivot position in every row, then the equation Ax=b has a solution
for each b in R™.
cannot have a pivot position in every row because it has more columns
D. This statement is false. If the augmented matrix [ A b] has a pivot position in every row, the equation Ax = b may or may not be
consistent. One pivot position may be in the column representing b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F799db758-6264-477e-875f-1cfecc426da7%2Fcee6a2ce-e9dd-43c1-8481-3364092cb9bb%2Fn0lc7o5k_processed.png&w=3840&q=75)
Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer.
The equation Ax=b is consistent if the augmented matrix [a b] has a pivot position in every row.
Choose the correct answer below.
C
A. This statement is false. The augmented matrix A b
than rows.
OB. This statement is true. The pivot positions in the augmented matrix [ A b] always occur in the columns that represent A.
OC. This statement is true. If the augmented matrix [ A b] has a pivot position in every row, then the equation Ax=b has a solution
for each b in R™.
cannot have a pivot position in every row because it has more columns
D. This statement is false. If the augmented matrix [ A b] has a pivot position in every row, the equation Ax = b may or may not be
consistent. One pivot position may be in the column representing b.
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