OpenCVの関数を使って連立方程式を解く

未知数が３つの３元連立方程式

2a + 2b + 3c = 15
3a + 5b + 2c = 19
5a + 3b + 3c = 20

OpenCVのMatの逆行列を計算する関数を使って，

#include <opencv2/opencv.hpp>

using namespace cv;
using std::cout;
using std::endl;

int main()
{
    Mat matA = (Mat_<float>(3,3) << 2, 2, 3, 3, 5, 2, 5, 3, 3);
    Mat matB = (Mat_<float>(3,1) << 15, 19, 20);
    Mat matX(3, 1, CV_32FC1);

    matX = matA.inv()*matB;

    cout << "a=" << matX.at<float>(0) << endl;
    cout << "b=" << matX.at<float>(1) << endl;
    cout << "c=" << matX.at<float>(2) << endl;
}

ちゃんと，a=1, b=2, c=3の解が出る．