Which of the following 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]. OC. 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 equation. vector 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.
Which of the following 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]. OC. 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 equation. vector 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
Related questions
Question
![Which of the
following statements are true? Remember that a
mathematical statement is said to be true if it is always true,
under all circumstances.
A. The equation Ax = b is consistent if the augmented
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 in Rm.
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%2F8a1ff5b0-6d62-4156-84f4-ecc9607dcad9%2F982b19ea-2be2-4693-8f8e-b2cc8c89a1ac%2Fl4086fc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Which of the
following statements are true? Remember that a
mathematical statement is said to be true if it is always true,
under all circumstances.
A. The equation Ax = b is consistent if the augmented
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 in Rm.
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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