Which of the Tollowing statements are true? Remember that a mathematical statement is said to be true if it is always true, under all circumstances. b is consistent if the augmented A. The equation Ax matrix A | b 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]. %3D |C. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x.
Which of the Tollowing statements are true? Remember that a mathematical statement is said to be true if it is always true, under all circumstances. b is consistent if the augmented A. The equation Ax matrix A | b 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]. %3D |C. Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x.
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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true or false
![Which of the
Tollowing statements are true? Remember that a
mathematical statement is said to be true if it is always true,
under all circumstances.
b is consistent if the augmented
A. The equation Ax
matrix A | b 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 az ].
%3D
|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 x n matrix whose columns do not span
R", then the equation Ax
b in R".
b is inconsistent for some
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4995523b-8218-4ff8-8dd8-6a73c1c8def5%2F6f9e4056-8ac6-4a29-9f33-5106afbcde73%2Fu8v82z4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Which of the
Tollowing statements are true? Remember that a
mathematical statement is said to be true if it is always true,
under all circumstances.
b is consistent if the augmented
A. The equation Ax
matrix A | b 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 az ].
%3D
|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 x n matrix whose columns do not span
R", then the equation Ax
b in R".
b is inconsistent for some
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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