Are the following statements true or false? ? ✓ 1. If the augmented matrix [A [b] has a pivot position in every row, then the system Ax=b is inconsistent. ✓2. The equation Ax=b is referred to as a vector equation. ? ? ? ? ? positi ? 3. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x ✓4. If the columns of an m x n matrix A span R™, then the equation Ax=b is consistent for each b in R™ 5. If the system Ax = b is inconsistent, then b is not in the column space of A. 6. If A is an m x n matrix and if the equation Ax=b is inconsistent for some b in R™, then the RREF of A cannot ha in every row. ✓ 7. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one so
Are the following statements true or false? ? ✓ 1. If the augmented matrix [A [b] has a pivot position in every row, then the system Ax=b is inconsistent. ✓2. The equation Ax=b is referred to as a vector equation. ? ? ? ? ? positi ? 3. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x ✓4. If the columns of an m x n matrix A span R™, then the equation Ax=b is consistent for each b in R™ 5. If the system Ax = b is inconsistent, then b is not in the column space of A. 6. If A is an m x n matrix and if the equation Ax=b is inconsistent for some b in R™, then the RREF of A cannot ha in every row. ✓ 7. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one so
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
In this problem, state whether each of the 7 statements are true or false. No explanation/work needed.
![Are the following statements true or false?
?
✓1. If the augmented matrix [A b] has a pivot position in every row, then the system Ax = b is inconsistent.
2. The equation Ax = b is referred to as a vector equation.
✓ 3. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x
✓ 4. If the columns of an m x n matrix A span R™, then the equation Ax=b is consistent for each b in IR™
5. If the system Ax = b is inconsistent, then b is not in the column space of A.
?
6. If A is an m x 7 matrix and if the equation Ax=b is inconsistent for some b in R™, then the RREF of A cannot have a pivot
position in every row.
7. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution.
?
?
?
?
?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9b94972-a426-4972-a4d5-443b28f6c1aa%2F1669e97e-6a6b-491c-8ae2-e96f5a67bc95%2Frqnwc5w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Are the following statements true or false?
?
✓1. If the augmented matrix [A b] has a pivot position in every row, then the system Ax = b is inconsistent.
2. The equation Ax = b is referred to as a vector equation.
✓ 3. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x
✓ 4. If the columns of an m x n matrix A span R™, then the equation Ax=b is consistent for each b in IR™
5. If the system Ax = b is inconsistent, then b is not in the column space of A.
?
6. If A is an m x 7 matrix and if the equation Ax=b is inconsistent for some b in R™, then the RREF of A cannot have a pivot
position in every row.
7. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution.
?
?
?
?
?
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