1. Describe the set of b for which the following system does have a solution. 21 + 2x2 + 2x3 = b₁ + 7x2 + 8x3 =b₂ 3x1 -21 + 2x3 b3 Give a specific example of a vector b for which the system has a solution. 2. Are the following linear systems possible? If it is possible for such a system to exist, give an example of an augmented row-reduced echelon matrix which satisfies the description. If it's not possible, explain why not. A. A linear system of 3 equations, 3 unknowns, with infinitely many solutions B. A linear system of 3 equations, 4 unknowns, with exactly one solution C. A linear system of 3 equations, 2 unknowns, with exactly one solution D. A linear system of 3 equations, 2 unknowns, with no solutions
1. Describe the set of b for which the following system does have a solution. 21 + 2x2 + 2x3 = b₁ + 7x2 + 8x3 =b₂ 3x1 -21 + 2x3 b3 Give a specific example of a vector b for which the system has a solution. 2. Are the following linear systems possible? If it is possible for such a system to exist, give an example of an augmented row-reduced echelon matrix which satisfies the description. If it's not possible, explain why not. A. A linear system of 3 equations, 3 unknowns, with infinitely many solutions B. A linear system of 3 equations, 4 unknowns, with exactly one solution C. A linear system of 3 equations, 2 unknowns, with exactly one solution D. A linear system of 3 equations, 2 unknowns, with no solutions
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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Transcribed Image Text:1. Describe the set of b for which the following system does have a solution.
21
+ 2x2 + 2x3 = b₁
3x1
+7x2 + 8x3 =
b₂
-21
+ 2x3 =
b3
Give a specific example of a vector b for which the system has a solution.
2. Are the following linear systems possible? If it is possible for such a system to exist, give an
example of an augmented row-reduced echelon matrix which satisfies the description. If it's not
possible, explain why not.
A. A linear system of 3 equations, 3 unknowns, with infinitely many solutions
B. A linear system of 3 equations, 4 unknowns, with exactly one solution
C. A linear system of 3 equations, 2 unknowns, with exactly one solution
D. A linear system of 3 equations, 2 unknowns, with no solutions
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