Solve the system of equations using matrices. Use the Gaussian elimination method with back-substitution. x + y z = -5 3x y + z = -7 -x + 3y - 2z = 1 Use the Gaussian elimination method to obtain the matrix in row-echelon form. Choose the correct answer below. OA. O C. ! 1 1 - 1 - 5 0 1 - 1-2 0 0 1 4 100-5 1 0 -2 4 - 1 - 1 1 1 ... The solution set is {10}. (Simplify your answers.) O B. O D. -1 -1 0 - 1 0 0 1 -5 1 -2 - 1 4 1 1-5 1 01-2 1 0 0 4 1
Solve the system of equations using matrices. Use the Gaussian elimination method with back-substitution. x + y z = -5 3x y + z = -7 -x + 3y - 2z = 1 Use the Gaussian elimination method to obtain the matrix in row-echelon form. Choose the correct answer below. OA. O C. ! 1 1 - 1 - 5 0 1 - 1-2 0 0 1 4 100-5 1 0 -2 4 - 1 - 1 1 1 ... The solution set is {10}. (Simplify your answers.) O B. O D. -1 -1 0 - 1 0 0 1 -5 1 -2 - 1 4 1 1-5 1 01-2 1 0 0 4 1
Solve the system of equations using matrices. Use the Gaussian elimination method with back-substitution. x + y z = -5 3x y + z = -7 -x + 3y - 2z = 1 Use the Gaussian elimination method to obtain the matrix in row-echelon form. Choose the correct answer below. OA. O C. ! 1 1 - 1 - 5 0 1 - 1-2 0 0 1 4 100-5 1 0 -2 4 - 1 - 1 1 1 ... The solution set is {10}. (Simplify your answers.) O B. O D. -1 -1 0 - 1 0 0 1 -5 1 -2 - 1 4 1 1-5 1 01-2 1 0 0 4 1
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Transcribed Image Text:**Solving Systems of Equations Using Matrices**
To solve the system of equations using matrices, we'll apply the Gaussian elimination method with back-substitution. Consider the following system:
\[
\begin{cases}
x + y - z = -5 \\
3x - y + z = -7 \\
-x + 3y - 2z = 1
\end{cases}
\]
**Objective:**
Use Gaussian elimination to transform the system into a row-echelon form matrix. Choose the correct matrix from the options provided.
**Options for Row-Echelon Form:**
- **Option A:**
\[
\begin{bmatrix}
1 & 1 & -1 & -5 \\
0 & 1 & -1 & -2 \\
0 & 0 & 1 & 4 \\
\end{bmatrix}
\]
- **Option B:**
\[
\begin{bmatrix}
-1 & -1 & 1 & -5 \\
0 & -1 & 1 & -2 \\
0 & 0 & -1 & 4 \\
\end{bmatrix}
\]
- **Option C:**
\[
\begin{bmatrix}
1 & 0 & 0 & -5 \\
-1 & 1 & 0 & -2 \\
-1 & 1 & 1 & 4 \\
\end{bmatrix}
\]
- **Option D:**
\[
\begin{bmatrix}
1 & 1 & -5 & -1 \\
0 & 1 & -2 & -1 \\
0 & 0 & 1 & 4 \\
\end{bmatrix}
\]
**Solution Set Format:**
Determine the solution set in the form \(\{ ( \Box , \Box , \Box ) \} \), simplifying your answers.
**Instructions:**
1. Use the Gaussian elimination to reduce the original matrix into the row-echelon form.
2. After achieving the row-echelon form, identify the correct matrix from the options.
3. Solve for \((x, y, z)\) using back-substitution to complete the solution set, ensuring simplification of the answers.
Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.
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![**Solving Systems of Equations Using Matrices**
To solve the system of equations using matrices, we'll apply the Gaussian elimination method with back-substitution. Consider the following system:
\[
\begin{cases}
x + y - z = -5 \\
3x - y + z = -7 \\
-x + 3y - 2z = 1
\end{cases}
\]
**Objective:**
Use Gaussian elimination to transform the system into a row-echelon form matrix. Choose the correct matrix from the options provided.
**Options for Row-Echelon Form:**
- **Option A:**
\[
\begin{bmatrix}
1 & 1 & -1 & -5 \\
0 & 1 & -1 & -2 \\
0 & 0 & 1 & 4 \\
\end{bmatrix}
\]
- **Option B:**
\[
\begin{bmatrix}
-1 & -1 & 1 & -5 \\
0 & -1 & 1 & -2 \\
0 & 0 & -1 & 4 \\
\end{bmatrix}
\]
- **Option C:**
\[
\begin{bmatrix}
1 & 0 & 0 & -5 \\
-1 & 1 & 0 & -2 \\
-1 & 1 & 1 & 4 \\
\end{bmatrix}
\]
- **Option D:**
\[
\begin{bmatrix}
1 & 1 & -5 & -1 \\
0 & 1 & -2 & -1 \\
0 & 0 & 1 & 4 \\
\end{bmatrix}
\]
**Solution Set Format:**
Determine the solution set in the form \(\{ ( \Box , \Box , \Box ) \} \), simplifying your answers.
**Instructions:**
1. Use the Gaussian elimination to reduce the original matrix into the row-echelon form.
2. After achieving the row-echelon form, identify the correct matrix from the options.
3. Solve for \((x, y, z)\) using back-substitution to complete the solution set, ensuring simplification of the answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc29afaca-2bcc-449e-b541-aa3eef827b4a%2F52411eda-f0af-429b-afa7-a1e6bf791457%2Fxhvc41a_processed.jpeg&w=3840&q=75)
