Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Exercise 18: Determining Consistency of a Linear System**
In Exercises 18, determine the value(s) of \( h \) such that the matrix is the augmented matrix of a consistent linear system.
\[
18. \quad \begin{bmatrix}
1 & -3 & -2 \\
5 & h & -7
\end{bmatrix}
\]
The problem presented involves a \(2 \times 3\) augmented matrix. The matrix is given as follows:
\[
\begin{bmatrix}
1 & -3 & -2 \\
5 & h & -7
\end{bmatrix}
\]
The goal is to find the value(s) of \( h \) such that the matrix represents a consistent linear system. This involves ensuring that the system of equations derived from the matrix has at least one solution.
To achieve this, you might consider row operations and conditions for consistency in linear systems.](https://content.bartleby.com/qna-images/question/bb1a8ba3-371b-48d7-95b6-c118f740fa83/d4c3e39b-9783-4df0-8cff-2918de12fb8d/wtvm05p_processed.png)
Transcribed Image Text:**Exercise 18: Determining Consistency of a Linear System**
In Exercises 18, determine the value(s) of \( h \) such that the matrix is the augmented matrix of a consistent linear system.
\[
18. \quad \begin{bmatrix}
1 & -3 & -2 \\
5 & h & -7
\end{bmatrix}
\]
The problem presented involves a \(2 \times 3\) augmented matrix. The matrix is given as follows:
\[
\begin{bmatrix}
1 & -3 & -2 \\
5 & h & -7
\end{bmatrix}
\]
The goal is to find the value(s) of \( h \) such that the matrix represents a consistent linear system. This involves ensuring that the system of equations derived from the matrix has at least one solution.
To achieve this, you might consider row operations and conditions for consistency in linear systems.
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