Given the linear system a) b) c) x₁ = x₂ + αx3 = -2 -x₁ + 2x₂ αx3 = 3 + x3 = 2 αx₁ + x₂ Find value(s) of a for which the system has no solutions. Find value(s) of a for which the system has an infinitely number of solutions. Assuming a unique solution exists for a given a, find the solution.
Given the linear system a) b) c) x₁ = x₂ + αx3 = -2 -x₁ + 2x₂ αx3 = 3 + x3 = 2 αx₁ + x₂ Find value(s) of a for which the system has no solutions. Find value(s) of a for which the system has an infinitely number of solutions. Assuming a unique solution exists for a given a, find the solution.
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
![**Given the linear system**
\[
\begin{align*}
x_1 - x_2 + \alpha x_3 &= -2 \\
-x_1 + 2x_2 - \alpha x_3 &= 3 \\
\alpha x_1 + x_2 + x_3 &= 2 \\
\end{align*}
\]
a) Find value(s) of \(\alpha\) for which the system has no solutions.
b) Find value(s) of \(\alpha\) for which the system has an infinitely number of solutions.
c) Assuming a unique solution exists for a given \(\alpha\), find the solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2f2c4bd-bf4c-4a3b-a0a2-6333c3306a45%2Feaa6314a-9332-4c1b-91f0-0c7a1cd66d7a%2F2oknv7j_processed.png&w=3840&q=75)
Transcribed Image Text:**Given the linear system**
\[
\begin{align*}
x_1 - x_2 + \alpha x_3 &= -2 \\
-x_1 + 2x_2 - \alpha x_3 &= 3 \\
\alpha x_1 + x_2 + x_3 &= 2 \\
\end{align*}
\]
a) Find value(s) of \(\alpha\) for which the system has no solutions.
b) Find value(s) of \(\alpha\) for which the system has an infinitely number of solutions.
c) Assuming a unique solution exists for a given \(\alpha\), find the solution.
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