Use NumPy to complete the following task(s). 2. Solve Assignment 4.1 #2a. 2. Consider the system x + ky = 1 x + y = 4, where k is a constant. where k is a constant. a. Solve the system for k = 0.99, k = 0.99999, k = 1.01, and k = 1.00001.
Use NumPy to complete the following task(s). 2. Solve Assignment 4.1 #2a. 2. Consider the system x + ky = 1 x + y = 4, where k is a constant. where k is a constant. a. Solve the system for k = 0.99, k = 0.99999, k = 1.01, and k = 1.00001.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Use Python
![### Solving Linear Systems with NumPy
#### Task Instructions
**2. Solve Assignment 4.1 #2a.**
**2. Consider the system of linear equations:**
\[ x + ky = 1 \]
\[ x + y = 4 \]
where \( k \) is a constant.
**a. Solve the system for \( k = 0.99 \), \( k = 0.99999 \), \( k = 1.01 \), and \( k = 1.00001 \).**
To solve this system of linear equations, we will utilize the NumPy library in Python. By substituting the given values of \( k \), we will find the solutions for the variables \( x \) and \( y \).
**Graphical Explanation (If required):**
To provide a deeper understanding, a graphical representation of the equations and their solutions for the different values of \( k \) might be helpful. Each value of \( k \) will slightly tilt the line \( x + ky = 1 \), and the point of intersection with the line \( x + y = 4 \) will give the solution for \( x \) and \( y \). This should be evident in the graphical plot showing the lines and their intersections for each given value of \( k \).
- For \( k = 0.99 \):
- Equation 1: \( x + 0.99y = 1 \)
- Equation 2: \( x + y = 4 \)
- For \( k = 0.99999 \):
- Equation 1: \( x + 0.99999y = 1 \)
- Equation 2: \( x + y = 4 \)
- For \( k = 1.01 \):
- Equation 1: \( x + 1.01y = 1 \)
- Equation 2: \( x + y = 4 \)
- For \( k = 1.00001 \):
- Equation 1: \( x + 1.00001y = 1 \)
- Equation 2: \( x + y = 4 \)
By solving these sets of equations, one can understand how slight variations in the parameter \( k \) affect the solutions of the system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea6ca246-da4e-4258-b850-8b268fd070fb%2F02c73fa1-f321-4475-ac4e-aff4697b21ed%2Flnzouwr_processed.png&w=3840&q=75)
Transcribed Image Text:### Solving Linear Systems with NumPy
#### Task Instructions
**2. Solve Assignment 4.1 #2a.**
**2. Consider the system of linear equations:**
\[ x + ky = 1 \]
\[ x + y = 4 \]
where \( k \) is a constant.
**a. Solve the system for \( k = 0.99 \), \( k = 0.99999 \), \( k = 1.01 \), and \( k = 1.00001 \).**
To solve this system of linear equations, we will utilize the NumPy library in Python. By substituting the given values of \( k \), we will find the solutions for the variables \( x \) and \( y \).
**Graphical Explanation (If required):**
To provide a deeper understanding, a graphical representation of the equations and their solutions for the different values of \( k \) might be helpful. Each value of \( k \) will slightly tilt the line \( x + ky = 1 \), and the point of intersection with the line \( x + y = 4 \) will give the solution for \( x \) and \( y \). This should be evident in the graphical plot showing the lines and their intersections for each given value of \( k \).
- For \( k = 0.99 \):
- Equation 1: \( x + 0.99y = 1 \)
- Equation 2: \( x + y = 4 \)
- For \( k = 0.99999 \):
- Equation 1: \( x + 0.99999y = 1 \)
- Equation 2: \( x + y = 4 \)
- For \( k = 1.01 \):
- Equation 1: \( x + 1.01y = 1 \)
- Equation 2: \( x + y = 4 \)
- For \( k = 1.00001 \):
- Equation 1: \( x + 1.00001y = 1 \)
- Equation 2: \( x + y = 4 \)
By solving these sets of equations, one can understand how slight variations in the parameter \( k \) affect the solutions of the system.
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