Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![Write the system of linear equations in the form \( Ax = b \) and solve this matrix equation for \( x \).
\[
\begin{align*}
x_1 - 5x_2 + 2x_3 &= -19 \\
-3x_1 + x_2 - x_3 &= 10 \\
-2x_2 + 5x_3 &= -11 \\
\end{align*}
\]
**Matrix Representation:**
The system can be represented in matrix form:
\[
\begin{bmatrix}
1 & -5 & 2 \\
-3 & 1 & -1 \\
0 & -2 & 5 \\
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
\end{bmatrix}
=
\begin{bmatrix}
-19 \\
10 \\
-11 \\
\end{bmatrix}
\]
Here, the first matrix is the coefficient matrix, the second column matrix represents the variables \(x_1\), \(x_2\), and \(x_3\), and the third column matrix is the constant matrix \(b\). To solve for \(x\), compute the inverse of the coefficient matrix and multiply it by the constant matrix.](https://content.bartleby.com/qna-images/question/c42b80bf-a5d4-414b-bce1-0fe52a04dbbd/1e7facd6-445c-47b7-86a1-008141e0fdd1/11789g_processed.png)
Transcribed Image Text:Write the system of linear equations in the form \( Ax = b \) and solve this matrix equation for \( x \).
\[
\begin{align*}
x_1 - 5x_2 + 2x_3 &= -19 \\
-3x_1 + x_2 - x_3 &= 10 \\
-2x_2 + 5x_3 &= -11 \\
\end{align*}
\]
**Matrix Representation:**
The system can be represented in matrix form:
\[
\begin{bmatrix}
1 & -5 & 2 \\
-3 & 1 & -1 \\
0 & -2 & 5 \\
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
\end{bmatrix}
=
\begin{bmatrix}
-19 \\
10 \\
-11 \\
\end{bmatrix}
\]
Here, the first matrix is the coefficient matrix, the second column matrix represents the variables \(x_1\), \(x_2\), and \(x_3\), and the third column matrix is the constant matrix \(b\). To solve for \(x\), compute the inverse of the coefficient matrix and multiply it by the constant matrix.
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