Introductory Circuit Analysis (13th Edition)
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ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Solve the matrix by hand.
![The image presents a system of linear equations in matrix form. The equation is structured as follows:
\[
\begin{bmatrix}
2 & -1 & 0 \\
2 & 3 & 1 \\
1 & 4 & 2 \\
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
\end{bmatrix}
=
\begin{bmatrix}
0 \\
11 \\
15 \\
\end{bmatrix}
\]
### Explanation:
- The leftmost matrix is a \(3 \times 3\) coefficient matrix. Each row corresponds to the coefficients of a linear equation.
- The middle matrix is a column matrix consisting of variables \(x_1\), \(x_2\), and \(x_3\).
- The rightmost matrix is a \(3 \times 1\) matrix representing the constants on the right-hand side of the equations.
This matrix equation can be expanded into the following system of linear equations:
1. \(2x_1 - x_2 = 0\)
2. \(2x_1 + 3x_2 + x_3 = 11\)
3. \(x_1 + 4x_2 + 2x_3 = 15\)
This representation is useful for solving systems of equations using various methods such as substitution, elimination, or matrix techniques like Gaussian elimination or matrix inversion.](https://content.bartleby.com/qna-images/question/11b54239-8e64-41df-bbac-e376c02f6bfa/6b392488-9017-42f4-b73a-f1b8b184460e/c66k6un_processed.png)
Transcribed Image Text:The image presents a system of linear equations in matrix form. The equation is structured as follows:
\[
\begin{bmatrix}
2 & -1 & 0 \\
2 & 3 & 1 \\
1 & 4 & 2 \\
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
\end{bmatrix}
=
\begin{bmatrix}
0 \\
11 \\
15 \\
\end{bmatrix}
\]
### Explanation:
- The leftmost matrix is a \(3 \times 3\) coefficient matrix. Each row corresponds to the coefficients of a linear equation.
- The middle matrix is a column matrix consisting of variables \(x_1\), \(x_2\), and \(x_3\).
- The rightmost matrix is a \(3 \times 1\) matrix representing the constants on the right-hand side of the equations.
This matrix equation can be expanded into the following system of linear equations:
1. \(2x_1 - x_2 = 0\)
2. \(2x_1 + 3x_2 + x_3 = 11\)
3. \(x_1 + 4x_2 + 2x_3 = 15\)
This representation is useful for solving systems of equations using various methods such as substitution, elimination, or matrix techniques like Gaussian elimination or matrix inversion.
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