Write the system of linear equations in the form Ax = b and solve this matrix equation for x. X1 5x2 + 2x3 = -19 - Зх1 + X2 - -2x2 + 5x3 X3 = 10 = -11 X1 -19 X2 10 X3 -11 X1 X2 X3
Write the system of linear equations in the form Ax = b and solve this matrix equation for x. X1 5x2 + 2x3 = -19 - Зх1 + X2 - -2x2 + 5x3 X3 = 10 = -11 X1 -19 X2 10 X3 -11 X1 X2 X3
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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2.1
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc42b80bf-a5d4-414b-bce1-0fe52a04dbbd%2F1e7facd6-445c-47b7-86a1-008141e0fdd1%2F11789g_processed.png&w=3840&q=75)
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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