Use loops to create a n x m matrix in which the value of each element is the its row number minus its column number divided by the cube of its row number. For example, the value of element (4,1) is (4 - 1)/4^3. The program should ask the user to enter values for n and m.
Use loops to create a n x m matrix in which the value of each element is the its row number minus its column number divided by the cube of its row number. For example, the value of element (4,1) is (4 - 1)/4^3. The program should ask the user to enter values for n and m.
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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![### Creating an NxM Matrix with Specific Element Values
**Objective:**
Use loops to create an NxM matrix where the value of each element is calculated based on its row and column numbers. The value of an element at position (i, j) is computed as:
\[ \text{Element}(i, j) = \frac{(i - j)}{i^3} \]
### Instructions:
1. **Gather Inputs:**
The program should prompt the user to enter values for N (number of rows) and M (number of columns).
2. **Matrix Initialization:**
Initialize a matrix with N rows and M columns.
3. **Compute Elements:**
Use nested loops to iterate over each element in the matrix. Calculate the value of each element using the formula provided.
4. **Example Calculation:**
- For an element at position (4, 1), the value is calculated as:
\[ \text{Element}(4, 1) = \frac{(4 - 1)}{4^3} \]
### Python Code Example:
```python
def create_matrix(n, m):
matrix = []
for i in range(1, n + 1):
row = []
for j in range(1, m + 1):
value = (i - j) / (i ** 3)
row.append(value)
matrix.append(row)
return matrix
# Gather user input for n and m
n = int(input("Enter the number of rows (n): "))
m = int(input("Enter the number of columns (m): "))
# Create the matrix
matrix = create_matrix(n, m)
# Display the matrix
for row in matrix:
print(row)
```
### Explanation:
- **Input:**
- The user inputs the number of rows (N) and columns (M).
- **Matrix Creation:**
- An empty matrix `matrix` is initialized.
- Nested loops run:
- The outer loop iterates over each row (variable `i`).
- The inner loop iterates over each column (variable `j`).
- For each element at position (i, j), the value is calculated with \(\frac{(i - j)}{i^3}\) and appended to the current row.
- Each completed row is appended to the matrix.
- **Output](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F885f4e27-5b29-4c6f-b568-f932f5320acb%2F10045a71-0d4b-438d-8de6-6e3e2bc0dee5%2Fhf6g2ao.jpeg&w=3840&q=75)
Transcribed Image Text:### Creating an NxM Matrix with Specific Element Values
**Objective:**
Use loops to create an NxM matrix where the value of each element is calculated based on its row and column numbers. The value of an element at position (i, j) is computed as:
\[ \text{Element}(i, j) = \frac{(i - j)}{i^3} \]
### Instructions:
1. **Gather Inputs:**
The program should prompt the user to enter values for N (number of rows) and M (number of columns).
2. **Matrix Initialization:**
Initialize a matrix with N rows and M columns.
3. **Compute Elements:**
Use nested loops to iterate over each element in the matrix. Calculate the value of each element using the formula provided.
4. **Example Calculation:**
- For an element at position (4, 1), the value is calculated as:
\[ \text{Element}(4, 1) = \frac{(4 - 1)}{4^3} \]
### Python Code Example:
```python
def create_matrix(n, m):
matrix = []
for i in range(1, n + 1):
row = []
for j in range(1, m + 1):
value = (i - j) / (i ** 3)
row.append(value)
matrix.append(row)
return matrix
# Gather user input for n and m
n = int(input("Enter the number of rows (n): "))
m = int(input("Enter the number of columns (m): "))
# Create the matrix
matrix = create_matrix(n, m)
# Display the matrix
for row in matrix:
print(row)
```
### Explanation:
- **Input:**
- The user inputs the number of rows (N) and columns (M).
- **Matrix Creation:**
- An empty matrix `matrix` is initialized.
- Nested loops run:
- The outer loop iterates over each row (variable `i`).
- The inner loop iterates over each column (variable `j`).
- For each element at position (i, j), the value is calculated with \(\frac{(i - j)}{i^3}\) and appended to the current row.
- Each completed row is appended to the matrix.
- **Output
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