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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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.
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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