A = [1  2  1 -3  2
     3  7  5 -7  10
    -2 -2  3  13 0
    -1  2  5  6  24
     4  10 9 -4  13];

b = [-8; -24; 9; 28; -35];

A = [A b];

U1 = [A b];

v = U1(1, :);
U1(1, :) = U1(5, :);
U1(5, :) = v;

#zerowanie kolumny 1
U1(2, :) = U1(2, :) - (U1(2, 1) / U1(1, 1))*U1(1, :);
U1(3, :) = U1(3, :) - (U1(3, 1) / U1(1, 1))*U1(1, :);
U1(4, :) = U1(4, :) - (U1(4, 1) / U1(1, 1))*U1(1, :);
U1(5, :) = U1(5, :) - (U1(5, 1) / U1(1, 1))*U1(1, :);

#maks w 2 kolumnie
maks = max(abs(U1(2:5, 2)));
#przestawianie wiersza
v1 = U1(2, :);
U1(2, :) = U1(4, :);
U1(4, :) = v1;

#zerowanie kolumny 2:
U1(3, :) = U1(3, :) - (U1(3, 2) / U1(2, 2))*U1(2, :);
U1(4, :) = U1(4, :) - (U1(4, 2) / U1(2, 2))*U1(2, :);
U1(5, :) = U1(5, :) - (U1(5, 2) / U1(2, 2))*U1(2, :);

#maks w 3 kolumnie
maks = max(abs(U1(3:5, 3)));
#zerowanie kolumny
U1(4, :) = U1(4, :) - (U1(4, 3) / U1(3, 3))*U1(3, :);
U1(5, :) = U1(5, :) - (U1(5, 3) / U1(3, 3))*U1(3, :);

#maks w 4 kolumnie !wartosc bezwgledna
maks = max(abs(U1(4:5, 4)));
#zerowanie kolumny 4:
U1(5, :) = U1(5, :) - (U1(5, 4) / U1(4, 4))*U1(4, :);

#U1 = A(1:5, 1:5);
b1 = U1(:, 6);