A. The equation Ax = b is consistent if the augmented matrix A | b] has a pivot position in every row. OB. The solution set of a linear system whose augmented matrix is a1 a2 az | 6| is the same as the solution set of = b, if A = [a1 az az . C. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x. ND. 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 Rm. E. The equation Ax = b is referred to as a vector equation. F. 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.
A. The equation Ax = b is consistent if the augmented matrix A | b] has a pivot position in every row. OB. The solution set of a linear system whose augmented matrix is a1 a2 az | 6| is the same as the solution set of = b, if A = [a1 az az . C. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x. ND. 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 Rm. E. The equation Ax = b is referred to as a vector equation. F. 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.
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
True or false
Transcribed Image Text:b is consistent if the augmented
DA. The equation Ax
matrix A| 6 has a pivot position in every row.
B. The solution set of a linear system whose augmented
matrix is a1 a2 az | b| is the same as the solution set of
Ax = b, if A = [a1 a2 a3 |.
|C. Any linear combination of vectors can always be
written in the form Ax for a suitable matrix A and vector
X.
D. 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".
E. The equation Ax = b is referred to as a vector
equation.
F. 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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