Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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".
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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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