Which of the following statements are true? (May contain one or more true statements, or none.) DA. If A is an m X n matrix whose columns do not span R", then the equation Ax = b is inconsistent for some b in R". DB. If the augmented matrix [ A b ] has a pivot position in every row, then the equation Ax = b is inconsistent. DC. The equation Ax = b is referred to as a vector equation. DD. If A is an m X n matrix and if the equation Ax = b is inconsistent for some b in R", then A cannot have a pivot position in every row. DE. 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. OF. If the columns of an m × n matrix A span R", then the equation Ax = b is consistent for each b in R".
Which of the following statements are true? (May contain one or more true statements, or none.) DA. If A is an m X n matrix whose columns do not span R", then the equation Ax = b is inconsistent for some b in R". DB. If the augmented matrix [ A b ] has a pivot position in every row, then the equation Ax = b is inconsistent. DC. The equation Ax = b is referred to as a vector equation. DD. If A is an m X n matrix and if the equation Ax = b is inconsistent for some b in R", then A cannot have a pivot position in every row. DE. 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. OF. If the columns of an m × n matrix A span R", then the equation Ax = b is consistent for each b in R".
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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![Which of the following statements are true? (May contain one or more true statements, or none.)
OA.
If A is an m X n matrix whose columns do not span R", then the equation Ax = b is inconsistent for some b in R".
В.
If the augmented matrix [ A b] has a pivot position in every row, then the equation Ax = b is inconsistent.
OC.
The equation Ax = b is referred to as a vector equation.
OD.
If A is an m X n matrix and if the equation Ax = b is inconsistent for some b in R", then A cannot have a pivot position in every row.
OE.
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.
OF.
If the columns of an m X n matrixA span R", then the equation Ax = b is consistent for each bin R".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef00a73d-c39f-498a-82ae-7c0ab24db4f8%2Fa323e8d8-e6aa-4df0-b68b-8c497f160c97%2F3brrezm_processed.png&w=3840&q=75)
Transcribed Image Text:Which of the following statements are true? (May contain one or more true statements, or none.)
OA.
If A is an m X n matrix whose columns do not span R", then the equation Ax = b is inconsistent for some b in R".
В.
If the augmented matrix [ A b] has a pivot position in every row, then the equation Ax = b is inconsistent.
OC.
The equation Ax = b is referred to as a vector equation.
OD.
If A is an m X n matrix and if the equation Ax = b is inconsistent for some b in R", then A cannot have a pivot position in every row.
OE.
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.
OF.
If the columns of an m X n matrixA span R", then the equation Ax = b is consistent for each bin R".
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