Solve the equation x H Y 2 = 8 + t 0 1 0 6x+6y1z = 0
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
![**Solve the Equation**
Given the linear equation:
\[6x + 6y - 1z = 0\]
You can express the solution in parametric form as a combination of a particular solution \( \mathbf{s} \) and a vector \( \mathbf{t} \) denoting the direction of free variables in the null space. This is illustrated below:
\[
\begin{bmatrix}
x \\
y \\
z
\end{bmatrix}
= \mathbf{s} + t \begin{bmatrix}
0 \\
1 \\
0
\end{bmatrix}
\]
Here, \( \mathbf{s} \) is a specific solution to the equation and \( \begin{bmatrix}
0 \\
1 \\
0
\end{bmatrix} \) is the direction vector along which solutions vary with the parameter \( t \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30a42a85-c58f-45ac-a4af-faeed1a599e1%2F978a22e9-3bdc-4c6d-8bd6-4a4149bb303a%2F9juy7vg_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve the Equation**
Given the linear equation:
\[6x + 6y - 1z = 0\]
You can express the solution in parametric form as a combination of a particular solution \( \mathbf{s} \) and a vector \( \mathbf{t} \) denoting the direction of free variables in the null space. This is illustrated below:
\[
\begin{bmatrix}
x \\
y \\
z
\end{bmatrix}
= \mathbf{s} + t \begin{bmatrix}
0 \\
1 \\
0
\end{bmatrix}
\]
Here, \( \mathbf{s} \) is a specific solution to the equation and \( \begin{bmatrix}
0 \\
1 \\
0
\end{bmatrix} \) is the direction vector along which solutions vary with the parameter \( t \).
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