1. Consider the system of equations with the following augmented matrix, in which a and b are real numbers. 02 a²3 b a b 0 1 0 0 a 0 0 0 6² a 4 (a) Find all values of a and b for which the system is inconsistent. Explain your answer. (b) For values of a and b for which the system is consistent, find its general solution and express your answer in the usual column form. Note that a and b are arbitrary here. Either of them could be zero, positive, or negative, and the system will likely have different solutions depending on their values. As a result, it's best to consider cases in which the values of a and b are in different ranges (for example, when a = 0 or a 0, and perhaps different possibilities for b within those). Describe your cases carefully and organize your solution neatly.
1. Consider the system of equations with the following augmented matrix, in which a and b are real numbers. 02 a²3 b a b 0 1 0 0 a 0 0 0 6² a 4 (a) Find all values of a and b for which the system is inconsistent. Explain your answer. (b) For values of a and b for which the system is consistent, find its general solution and express your answer in the usual column form. Note that a and b are arbitrary here. Either of them could be zero, positive, or negative, and the system will likely have different solutions depending on their values. As a result, it's best to consider cases in which the values of a and b are in different ranges (for example, when a = 0 or a 0, and perhaps different possibilities for b within those). Describe your cases carefully and organize your solution neatly.
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. Consider the system of equations with the following augmented matrix, in which a and b are real numbers.
02 a² 3
a b 0 1
00 a
1
0
0
b
a
06² 4
(a) Find all values of a and b for which the system is inconsistent. Explain your answer.
(b) For values of a and b for which the system is consistent, find its general solution and express your answer
in the usual column form.
Note that a and b are arbitrary here. Either of them could be zero, positive, or negative, and the system
will likely have different solutions depending on their values. As a result, it's best to consider cases in
which the values of a and 6 are in different ranges (for example, when a = 0 or a 0, and perhaps
different possibilities for b within those).
Describe your cases carefully and organize your solution neatly.
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