The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the system. 100-5 0 10 0 0 0 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The system has exactly one solution. The solution is ( ID. (Type integers or fractions.) O B. The system has infinitely many solutions of the form ( z), where z is any real number. (Type integers or fractions.) OC. The system has no solution. 576
The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the system. 100-5 0 10 0 0 0 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The system has exactly one solution. The solution is ( ID. (Type integers or fractions.) O B. The system has infinitely many solutions of the form ( z), where z is any real number. (Type integers or fractions.) OC. The system has no solution. 576
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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![### Solving Systems of Equations Using Matrices
The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the system.
\[
\begin{bmatrix}
1 & 0 & 0 & | & -5 \\
0 & 1 & 0 & | & 7 \\
0 & 0 & 0 & | & 6
\end{bmatrix}
\]
### Multiple Choice Question
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
- **A.** The system has exactly one solution. The solution is \(( \_\_, \_\_ )\).
(Type integers or fractions.)
- **B.** The system has infinitely many solutions of the form \(( \_\_, \_\_, z )\), where \(z\) is any real number.
(Type integers or fractions.)
- **C.** The system has no solution.
### Analysis of the Augmented Matrix
- The matrix is in reduced row echelon form (RREF).
- The third row: \([0 \quad 0 \quad 0 \quad | \quad 6]\) indicates an inconsistency in the system (since \(0 \neq 6\)).
Thus, the system has no solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57708f6a-cbd4-4295-9f28-330268fec57a%2Ffb23fc58-8ad4-4280-9402-f809c4d4e15c%2Ffj0tnmj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Systems of Equations Using Matrices
The reduced row echelon form of the augmented matrix of a system of equations is given. Find the solutions of the system.
\[
\begin{bmatrix}
1 & 0 & 0 & | & -5 \\
0 & 1 & 0 & | & 7 \\
0 & 0 & 0 & | & 6
\end{bmatrix}
\]
### Multiple Choice Question
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
- **A.** The system has exactly one solution. The solution is \(( \_\_, \_\_ )\).
(Type integers or fractions.)
- **B.** The system has infinitely many solutions of the form \(( \_\_, \_\_, z )\), where \(z\) is any real number.
(Type integers or fractions.)
- **C.** The system has no solution.
### Analysis of the Augmented Matrix
- The matrix is in reduced row echelon form (RREF).
- The third row: \([0 \quad 0 \quad 0 \quad | \quad 6]\) indicates an inconsistency in the system (since \(0 \neq 6\)).
Thus, the system has no solution.
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