Write the 3x - 7y = 8 7x - 5y = 2 X 8 D-A y 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![### Writing a System of Linear Equations in Matrix Form
To express a given system of linear equations in matrix form, follow these steps:
Given the system of linear equations:
\[ 3x - 7y = 8 \]
\[ 7x - 5y = 2 \]
We can convert this into a matrix equation of the form \( A \mathbf{x} = \mathbf{b} \), where:
- \( A \) is the matrix of coefficients.
- \( \mathbf{x} \) is the column matrix of variables.
- \( \mathbf{b} \) is the column matrix of constants.
#### Step-by-Step Conversion:
1. Identify the coefficients of the variables in the equations:
- From the equation \( 3x - 7y = 8 \), the coefficients are 3 and -7.
- From the equation \( 7x - 5y = 2 \), the coefficients are 7 and -5.
2. Construct the coefficient matrix \( A \):
\[ A = \begin{bmatrix}
3 & -7 \\
7 & -5
\end{bmatrix} \]
3. Construct the variable matrix \( \mathbf{x} \):
\[ \mathbf{x} = \begin{bmatrix}
x \\
y
\end{bmatrix} \]
4. Construct the constants matrix \( \mathbf{b} \):
\[ \mathbf{b} = \begin{bmatrix}
8 \\
2
\end{bmatrix} \]
5. Combine these matrices into the matrix equation:
\[ \begin{bmatrix}
3 & -7 \\
7 & -5
\end{bmatrix}
\begin{bmatrix}
x \\
y
\end{bmatrix}
= \begin{bmatrix}
8 \\
2
\end{bmatrix} \]
### Summary of the Image:
The image shows instructions and an example converting a system of linear equations into matrix form. The equations provided are \( 3x - 7y = 8 \) and \( 7x - 5y = 2 \), followed by an incomplete matrix setup. The correct matrix representation is:
\[ \begin{bmatrix}
3 & -7 \\
7 & -5
\end{bmatrix}
\begin{bmatrix}
x \\
y
\end{bmatrix}
= \begin](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e1b5fc2-7275-49e6-a434-e3b12d2d745f%2F66c6c05b-194f-402d-800e-748410de3440%2Fp3xo2fk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Writing a System of Linear Equations in Matrix Form
To express a given system of linear equations in matrix form, follow these steps:
Given the system of linear equations:
\[ 3x - 7y = 8 \]
\[ 7x - 5y = 2 \]
We can convert this into a matrix equation of the form \( A \mathbf{x} = \mathbf{b} \), where:
- \( A \) is the matrix of coefficients.
- \( \mathbf{x} \) is the column matrix of variables.
- \( \mathbf{b} \) is the column matrix of constants.
#### Step-by-Step Conversion:
1. Identify the coefficients of the variables in the equations:
- From the equation \( 3x - 7y = 8 \), the coefficients are 3 and -7.
- From the equation \( 7x - 5y = 2 \), the coefficients are 7 and -5.
2. Construct the coefficient matrix \( A \):
\[ A = \begin{bmatrix}
3 & -7 \\
7 & -5
\end{bmatrix} \]
3. Construct the variable matrix \( \mathbf{x} \):
\[ \mathbf{x} = \begin{bmatrix}
x \\
y
\end{bmatrix} \]
4. Construct the constants matrix \( \mathbf{b} \):
\[ \mathbf{b} = \begin{bmatrix}
8 \\
2
\end{bmatrix} \]
5. Combine these matrices into the matrix equation:
\[ \begin{bmatrix}
3 & -7 \\
7 & -5
\end{bmatrix}
\begin{bmatrix}
x \\
y
\end{bmatrix}
= \begin{bmatrix}
8 \\
2
\end{bmatrix} \]
### Summary of the Image:
The image shows instructions and an example converting a system of linear equations into matrix form. The equations provided are \( 3x - 7y = 8 \) and \( 7x - 5y = 2 \), followed by an incomplete matrix setup. The correct matrix representation is:
\[ \begin{bmatrix}
3 & -7 \\
7 & -5
\end{bmatrix}
\begin{bmatrix}
x \\
y
\end{bmatrix}
= \begin
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
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
