Найти произведение вектора на матрицу

#include <iostream>
#include <cmath>
using namespace std;
int main() {
    system("chcp 1251>nul");
    int n;
    cout << "size matrix and vector:"; cin >> n;
    double** a = new double* [n];
    cout << "Input matrix:" << endl;
    for (int i = 0; i < n; i++) {
        a[i] = new double[n];
        for (int j = 0; j < n; j++) {
            cout << "a[" << i + 1 << "][" << j + 1 << "] = "; cin >> a[i][j];
        }
    }
    double* b = new double[n];
    cout << "Input vector:" << endl;
    for (int i = 0; i < n; i++) {
        cout << "b[" << i + 1 << "] = "; cin >> b[i];
    }
    cout << "Matrix:" << endl;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            cout <<  a[i][j]<<" ";
        }
        cout << endl;
    }
    cout << "Vector: " << endl;
    for (int i = 0; i < n; i++) {
        cout <<  b[i]<<" ";
    }
    cout << endl;
    double* result = new double[n];
    for (int i = 0; i < n; i++)
    {
        result[i] = 0;
        for (int j = 0; j < n; j++)
        {
            result[i] += a[i][j] * b[j];
        }
    }
    cout << "Result:" << endl;
    for (int i = 0; i < n; i++) {
        cout << result[i] << " ";
    }
    cout << endl;
    for (int i = 0; i < n; i++) { delete a[i]; }
    delete[]a;
    delete[]b;
    delete[]result;
    system("pause>nul");
    return 0;
 
}