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
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Chapter2: Second-order Linear Odes
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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"
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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