Choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. x₁ +hx₂ = 3 2x₁ +4x₂ = k a. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.) A. The system has no solutions only when h and k
Choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. x₁ +hx₂ = 3 2x₁ +4x₂ = k a. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.) A. The system has no solutions only when h and k
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.1: Matrix Operations
Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...
Related questions
Question
PLEASE SOLVE BOTH I WILL GIVE THUMBS UP!!! PLEASEEE
![**Title: Solving Systems of Linear Equations**
**Introduction**
In this exercise, we will analyze the conditions under which a system of linear equations has no solution, a unique solution, or many solutions. Consider the following system of equations:
\[ x_1 + h x_2 = 3 \]
\[ 2x_1 + 4x_2 = k \]
---
**Exercise**
*Choose \( h \) and \( k \) such that the system has (a) no solution, (b) a unique solution, and (c) many solutions.*
**Question:**
a. **Select the correct answer below and fill in the answer box(es) to complete your choice.**
(Type an integer or simplified fraction.)
**Options:**
- **A.** The system has no solutions only when \( h \neq \) [ ] and \( k \neq \) [ ].
- **B.** The system has no solutions only when \( h = \) [ ] and \( k \) is any real number.
- **C.** The system has no solutions only when \( h \neq \) [ ] and \( k = \) [ ].
- **D.** The system has no solutions only when \( h \neq \) [ ] and \( k \) is any real number.
- **E.** The system has no solutions only when \( h \neq \) [ ] and \( h \) is any real number.
- **F.** The system has no solutions only when \( k = \) [ ] and \( h \) is any real number.
- **G.** The system has no solutions only when \( h = \) [ ] and \( k = \) [ ].
- **H.** The system has no solutions only when \( h = \) [ ] and \( k \neq \) [ ].
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c3522a4-50b1-4726-a83e-d332776e45d2%2F09667459-8b79-49fa-a86e-e997f9e1cd5a%2Fiwrlwpr_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Solving Systems of Linear Equations**
**Introduction**
In this exercise, we will analyze the conditions under which a system of linear equations has no solution, a unique solution, or many solutions. Consider the following system of equations:
\[ x_1 + h x_2 = 3 \]
\[ 2x_1 + 4x_2 = k \]
---
**Exercise**
*Choose \( h \) and \( k \) such that the system has (a) no solution, (b) a unique solution, and (c) many solutions.*
**Question:**
a. **Select the correct answer below and fill in the answer box(es) to complete your choice.**
(Type an integer or simplified fraction.)
**Options:**
- **A.** The system has no solutions only when \( h \neq \) [ ] and \( k \neq \) [ ].
- **B.** The system has no solutions only when \( h = \) [ ] and \( k \) is any real number.
- **C.** The system has no solutions only when \( h \neq \) [ ] and \( k = \) [ ].
- **D.** The system has no solutions only when \( h \neq \) [ ] and \( k \) is any real number.
- **E.** The system has no solutions only when \( h \neq \) [ ] and \( h \) is any real number.
- **F.** The system has no solutions only when \( k = \) [ ] and \( h \) is any real number.
- **G.** The system has no solutions only when \( h = \) [ ] and \( k = \) [ ].
- **H.** The system has no solutions only when \( h = \) [ ] and \( k \neq \) [ ].
---
![## Finding the General Solution of a System
### Problem Statement
Find the general solution of the system whose augmented matrix is given below:
\[
\begin{pmatrix}
1 & -2 & 0 & -1 & 0 & -9 \\
0 & 1 & 0 & 0 & -7 & 2 \\
0 & 0 & 0 & 1 & 6 & 7 \\
0 & 0 & 0 & 0 & 0 & 0 \\
\end{pmatrix}
\]
### Solution Choices
Select the correct choice below and, if necessary, fill in the answer boxes to complete your answer.
#### Option A
\[
\begin{cases}
x_1 = \boxed{\phantom{0}} \\
x_2 \text{ is free} \\
x_3 = \boxed{\phantom{0}} \\
x_4 \text{ is free} \\
x_5 \text{ is free}
\end{cases}
\]
#### Option B
\[
\begin{cases}
x_1 = \boxed{\phantom{0}} \\
x_2 = \boxed{\phantom{0}} \\
x_3 \text{ is free} \\
x_4 = \boxed{\phantom{0}} \\
x_5 \text{ is free}
\end{cases}
\]
#### Option C
\[
\begin{cases}
x_1 = \boxed{\phantom{0}} \\
x_2 = \boxed{\phantom{0}} \\
x_3 \text{ is free} \\
x_4 = \boxed{\phantom{0}} \\
x_5 = \boxed{\phantom{0}}
\end{cases}
\]
#### Option D
The system is inconsistent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c3522a4-50b1-4726-a83e-d332776e45d2%2F09667459-8b79-49fa-a86e-e997f9e1cd5a%2Fy42po4h_processed.png&w=3840&q=75)
Transcribed Image Text:## Finding the General Solution of a System
### Problem Statement
Find the general solution of the system whose augmented matrix is given below:
\[
\begin{pmatrix}
1 & -2 & 0 & -1 & 0 & -9 \\
0 & 1 & 0 & 0 & -7 & 2 \\
0 & 0 & 0 & 1 & 6 & 7 \\
0 & 0 & 0 & 0 & 0 & 0 \\
\end{pmatrix}
\]
### Solution Choices
Select the correct choice below and, if necessary, fill in the answer boxes to complete your answer.
#### Option A
\[
\begin{cases}
x_1 = \boxed{\phantom{0}} \\
x_2 \text{ is free} \\
x_3 = \boxed{\phantom{0}} \\
x_4 \text{ is free} \\
x_5 \text{ is free}
\end{cases}
\]
#### Option B
\[
\begin{cases}
x_1 = \boxed{\phantom{0}} \\
x_2 = \boxed{\phantom{0}} \\
x_3 \text{ is free} \\
x_4 = \boxed{\phantom{0}} \\
x_5 \text{ is free}
\end{cases}
\]
#### Option C
\[
\begin{cases}
x_1 = \boxed{\phantom{0}} \\
x_2 = \boxed{\phantom{0}} \\
x_3 \text{ is free} \\
x_4 = \boxed{\phantom{0}} \\
x_5 = \boxed{\phantom{0}}
\end{cases}
\]
#### Option D
The system is inconsistent.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
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
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
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
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
