Mark each statement True or False. Justify each answer. (a) If the equation Ax = b is inconsistent, then b is not in the set spanned by the columns of A. (b) If the augmented matrix [A b] has a pivot position in every row, then the equa- tion Ax = b is inconsistent. (c) If A is an m x n matrix whose columns do not span R" , then the equation Ax is inconsistent for some b in R"
Mark each statement True or False. Justify each answer. (a) If the equation Ax = b is inconsistent, then b is not in the set spanned by the columns of A. (b) If the augmented matrix [A b] has a pivot position in every row, then the equa- tion Ax = b is inconsistent. (c) If A is an m x n matrix whose columns do not span R" , then the equation Ax is inconsistent for some 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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![9.
Mark each statement True or False. Justify each answer.
b is inconsistent, then b is not in the set spanned by the
(a) If the equation Ax
columns of A.
(b) If the augmented matrix [A b] has a pivot position in every row, then the
tion Ax = b is inconsistent.
equa-
(c) If A is an m × n matrix whose columns do not span R" , then the equation Ax = b
is inconsistent for some b in R"](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47353426-112c-4f9c-bd7c-673f33f0acc1%2F9d2745cd-f115-4a90-9f28-d91ffb9564ea%2F1atu1m_processed.png&w=3840&q=75)
Transcribed Image Text:9.
Mark each statement True or False. Justify each answer.
b is inconsistent, then b is not in the set spanned by the
(a) If the equation Ax
columns of A.
(b) If the augmented matrix [A b] has a pivot position in every row, then the
tion Ax = b is inconsistent.
equa-
(c) If A is an m × n matrix whose columns do not span R" , then the equation Ax = b
is inconsistent for some b in R"
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