Write the system of equations as an augmented matrix b 4y + 3u - 18 -b + Ty 3u 30 5b 2u L Ay || - 16
Write the system of equations as an augmented matrix b 4y + 3u - 18 -b + Ty 3u 30 5b 2u L Ay || - 16
Chapter4: Systems Of Linear Equations
Section4.4: Solve Systems Of Equations With Three Variables
Problem 4.66TI: Solve: {4x3z=53y+2z=73x+4y=6 .
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![**Transcription:**
**Title:** Write the System of Equations as an Augmented Matrix
**System of Equations:**
\[
\begin{align*}
-b - 4y + 3u &= -18 \\
-b + 7y - 3u &= 30 \\
5b - 4y - 2u &= -16 \\
\end{align*}
\]
**Explanation:**
The task is to express the above system of equations as an augmented matrix. An augmented matrix represents a system of linear equations, with each row corresponding to an equation, and the coefficients of each variable placed in columns. The rightmost column contains the constants from the right-hand side of the equations.
**Matrix Layout:**
The augmented matrix for the given system of equations is structured as follows:
\[
\begin{bmatrix}
-1 & -4 & 3 & \vert & -18 \\
-1 & 7 & -3 & \vert & 30 \\
5 & -4 & -2 & \vert & -16 \\
\end{bmatrix}
\]
**Diagram Description:**
Below the transcription of the system of equations, a graphical layout with empty rectangular boxes is depicted for where entries of an augmented matrix might be filled in by the user, illustrating the process of constructing the matrix with interactive tools.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F410204a0-8764-4473-a9c2-14bad68c17f5%2F8bfe2fd1-d71a-44c5-a0c9-2e4f4fb349a5%2Ftqmx028_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription:**
**Title:** Write the System of Equations as an Augmented Matrix
**System of Equations:**
\[
\begin{align*}
-b - 4y + 3u &= -18 \\
-b + 7y - 3u &= 30 \\
5b - 4y - 2u &= -16 \\
\end{align*}
\]
**Explanation:**
The task is to express the above system of equations as an augmented matrix. An augmented matrix represents a system of linear equations, with each row corresponding to an equation, and the coefficients of each variable placed in columns. The rightmost column contains the constants from the right-hand side of the equations.
**Matrix Layout:**
The augmented matrix for the given system of equations is structured as follows:
\[
\begin{bmatrix}
-1 & -4 & 3 & \vert & -18 \\
-1 & 7 & -3 & \vert & 30 \\
5 & -4 & -2 & \vert & -16 \\
\end{bmatrix}
\]
**Diagram Description:**
Below the transcription of the system of equations, a graphical layout with empty rectangular boxes is depicted for where entries of an augmented matrix might be filled in by the user, illustrating the process of constructing the matrix with interactive tools.
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