Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter11: Matrices And Determinants
Section11.CR: Chapter Review
Problem 4CC
Related questions
Question
100%
Please answer both!! THANK YOU!!
![### General Solution of System with Augmented Matrix
**Problem Statement:**
Find the general solution of the system whose augmented matrix is given below.
\[
\begin{bmatrix}
1 & 4 & 4 & 13 \\
2 & 8 & 5 & 14
\end{bmatrix}
\]
---
**Instruction:**
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
---
**Choices:**
- **A.**
\[
\begin{cases}
x_1 = \_\_\_ \\
x_2 \text{ is free} \\
x_3 \text{ is free}
\end{cases}
\]
- **B.**
\[
\begin{cases}
x_1 = \_\_\_ \\
x_2 = \_\_\_ \\
x_3 = \_\_\_
\end{cases}
\]
- **C.** **(*selected choice*)**
\[
\begin{cases}
x_1 = \_\_\_ \\
x_2 \text{ is free} \\
x_3 = \_\_\_
\end{cases}
\]
- **D.**
\[
\text{The system has no solution.}
\]
---
By determining the correct option, you will be able to write out the general solution for the given system of equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c3522a4-50b1-4726-a83e-d332776e45d2%2F0d49512a-0737-445e-9afd-17ecd55552f7%2Fsdd531i_processed.png&w=3840&q=75)
Transcribed Image Text:### General Solution of System with Augmented Matrix
**Problem Statement:**
Find the general solution of the system whose augmented matrix is given below.
\[
\begin{bmatrix}
1 & 4 & 4 & 13 \\
2 & 8 & 5 & 14
\end{bmatrix}
\]
---
**Instruction:**
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
---
**Choices:**
- **A.**
\[
\begin{cases}
x_1 = \_\_\_ \\
x_2 \text{ is free} \\
x_3 \text{ is free}
\end{cases}
\]
- **B.**
\[
\begin{cases}
x_1 = \_\_\_ \\
x_2 = \_\_\_ \\
x_3 = \_\_\_
\end{cases}
\]
- **C.** **(*selected choice*)**
\[
\begin{cases}
x_1 = \_\_\_ \\
x_2 \text{ is free} \\
x_3 = \_\_\_
\end{cases}
\]
- **D.**
\[
\text{The system has no solution.}
\]
---
By determining the correct option, you will be able to write out the general solution for the given system of equations.
![### Find the General Solution of the System with the Given Augmented Matrix
The augmented matrix for the system is given below:
\[
\begin{bmatrix}
0 & 1 & -4 & 3 \\
1 & -3 & 8 & -4
\end{bmatrix}
\]
---
### Choose the Correct Solution
Select the correct choice below and, if necessary, fill in any answer boxes to complete your answer.
A.
\[
\left\{
\begin{array}{l}
x_1 = \square \\
x_2 = \square \\
x_3 \text{ is free}
\end{array}
\right.
\]
B.
\[
\left\{
\begin{array}{l}
x_1 = \square \\
x_2 = \square \\
x_3 = \square
\end{array}
\right.
\]
C.
\[
\left\{
\begin{array}{l}
x_1 = \square \\
x_2 \text{ is free} \\
x_3 \text{ is free}
\end{array}
\right.
\]
D.
The system has no solution.
---
In each case, fill in the blanks where indicated for the variables \(x_1\), \(x_2\), and \(x_3\), or select the statement that the system has no solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c3522a4-50b1-4726-a83e-d332776e45d2%2F0d49512a-0737-445e-9afd-17ecd55552f7%2Fu7ttd0v_processed.png&w=3840&q=75)
Transcribed Image Text:### Find the General Solution of the System with the Given Augmented Matrix
The augmented matrix for the system is given below:
\[
\begin{bmatrix}
0 & 1 & -4 & 3 \\
1 & -3 & 8 & -4
\end{bmatrix}
\]
---
### Choose the Correct Solution
Select the correct choice below and, if necessary, fill in any answer boxes to complete your answer.
A.
\[
\left\{
\begin{array}{l}
x_1 = \square \\
x_2 = \square \\
x_3 \text{ is free}
\end{array}
\right.
\]
B.
\[
\left\{
\begin{array}{l}
x_1 = \square \\
x_2 = \square \\
x_3 = \square
\end{array}
\right.
\]
C.
\[
\left\{
\begin{array}{l}
x_1 = \square \\
x_2 \text{ is free} \\
x_3 \text{ is free}
\end{array}
\right.
\]
D.
The system has no solution.
---
In each case, fill in the blanks where indicated for the variables \(x_1\), \(x_2\), and \(x_3\), or select the statement that the system has no solution.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 18 images
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
