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. VA. 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 = [aj a2 a3 ]. VB. 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. VC. 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 in every row. OD. The equation Ax = b is referred to as a vector equation. VE. If the augmented matrix [ A | b] has a pivot position in every row, then the equation Ax = b is inconsistent. OF. The first entry in the product Ax is a sum of products.
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. VA. 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 = [aj a2 a3 ]. VB. 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. VC. 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 in every row. OD. The equation Ax = b is referred to as a vector equation. VE. If the augmented matrix [ A | b] has a pivot position in every row, then the equation Ax = b is inconsistent. OF. The first entry in the product Ax is a sum of products.
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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![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.
VA. The solution set of a linear system whose augmented matrix is aj az az | 6 is the same as the solution set of
Ах — b, if A — [ај ар аз |-
V B. 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.
VC. If A is an m × n matrix and if the equation Ax = b is inconsistent for some b in R", then A cannot have a pivot in
every row.
D. The equation Ax = b is referred to as a vector equation.
VE. If the augmented matrix A | b] has a pivot position in every row, then the equation Ax = b is inconsistent.
O F. The first entry in the product Ax is a sum of products.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc379e4a-fd2d-4da2-a6fa-d5a4af937453%2Ff68fba20-1eea-4cb5-8e45-c9b1989d7511%2Fmugnl5r_processed.png&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.
VA. The solution set of a linear system whose augmented matrix is aj az az | 6 is the same as the solution set of
Ах — b, if A — [ај ар аз |-
V B. 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.
VC. If A is an m × n matrix and if the equation Ax = b is inconsistent for some b in R", then A cannot have a pivot in
every row.
D. The equation Ax = b is referred to as a vector equation.
VE. If the augmented matrix A | b] has a pivot position in every row, then the equation Ax = b is inconsistent.
O F. The first entry in the product Ax is a sum of products.
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