-. Determine the values of a for which the system x + 2y3z = 4 3x = y + 5z = 2 4x + y + (a²-14)z = a + 2 has no solutions, exactly one solution, or infinitely many solutions.
-. Determine the values of a for which the system x + 2y3z = 4 3x = y + 5z = 2 4x + y + (a²-14)z = a + 2 has no solutions, exactly one solution, or infinitely many solutions.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Determine the values of \( a \) for which the system
\[
\begin{align*}
x + 2y - 3z &= 4 \\
3x - y + 5z &= 2 \\
4x + y + (a^2 - 14)z &= a + 2
\end{align*}
\]
has no solutions, exactly one solution, or infinitely many solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ebe91de-3090-46ac-907f-d0393c4d1db8%2F60660b33-dd76-4c8b-9614-0b644ad50a41%2Fcqpsa0u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determine the values of \( a \) for which the system
\[
\begin{align*}
x + 2y - 3z &= 4 \\
3x - y + 5z &= 2 \\
4x + y + (a^2 - 14)z &= a + 2
\end{align*}
\]
has no solutions, exactly one solution, or infinitely many solutions.
Expert Solution
Step 1l
The given system is ,
rewrite the given system in the form ; where is a coefficient matrix of order , is an vector and is an vector .
=>
And the augmented matrix of the system is .
Then the augment matrix of the given system is ,
=>
The given system has 3 unknown variables.
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