AUT_AP_2024_Spring_HW1

```cpp
// C++ Matrix Operations Module

#include <iostream>
#include <vector>

namespace algebra {
    // Matrix class definition
    class Matrix {
    public:
        Matrix(int rows, int cols);
        ~Matrix();
        // Matrix operations
        Matrix add(const Matrix& other) const;
        Matrix subtract(const Matrix& other) const;
        Matrix multiply(const Matrix& other) const;
    private:
        int rows;
        int cols;
        double** data;
    };

    // Constructor implementation
    Matrix::Matrix(int r, int c) : rows(r), cols(c) {
        data = new double*[rows];
        for (int i = 0; i < rows; ++i) {
            data[i] = new double[cols]();
        }
    }

    // Destructor implementation
    Matrix::~Matrix() {
        for (int i = 0; i < rows; ++i) {
            delete[] data[i];
        }
        delete[] data;
    }

    // Matrix addition implementation
    Matrix Matrix::add(const Matrix& other) const {
        if (rows != other.rows || cols != other.cols) {
            throw std::invalid_argument("Matrix dimensions do not match");
        }
        Matrix result(rows, cols);
        for (int i = 0; i < rows; ++i) {
            for (int j = 0; j < cols; ++j) {
                result.data[i][j] = data[i][j] + other.data[i][j];
            }
        }
        return result;
    }

    // Similar implementations for subtract and multiply
}

int main() {
    // Example usage
    algebra::Matrix m1(2, 2);
    algebra::Matrix m2(2, 2);
    algebra::Matrix m3 = m1.add(m2);
    return 0;
}
```

```bash
#!/bin/bash

# Directory Backup and Logging Script

# Configuration
BACKUP_DIR="/path/to/backup"
LOG_FILE="/var/log/backup.log"
SOURCE_DIRS=("/path/to/source1" "/path/to/source2")

# Logging function
log() {
    echo "[$(date +'%Y-%m-%d %H:%M:%S')] $1" >> "$LOG_FILE"
}

# Backup function
backup() {
    local dir=$1
    local timestamp=$(date +%Y%m%d_%H%M%S)
    local backup_file="$BACKUP_DIR/backup_${timestamp}.tar.gz"

    log "Starting backup of $dir"
    if tar -czf "$backup_file" "$dir" 2>> "$LOG_FILE"; then
        log "Backup of $dir completed successfully"
    else
        log "Error: Backup of $dir failed"
        return 1
    fi
}

# Main script
log "Backup script started"

for dir in "${SOURCE_DIRS[@]}"; do
    if [ -d "$dir" ]; then
        backup "$dir"
    else
        log "Error: Source directory $dir does not exist"
    fi
done

log "Backup script finished"
```