Task1
Is matrix A equal to matrix B?
True
Matrix A multiplied with 3.14159265359
Matrix A divided with 3.14159265359
Is matrix A equal to itself after multiplication and division with real number?
True
------------------
Task2
LU decomposition:
Impossible to perform LU decomposition because pivot element is too small for division!
LUP decomposition:
Lower:
      0    1  2
0  1.00  0.0  0
1  0.25  1.0  0
2  0.75 -0.0  1
Upper:
     0     1     2
0  4.0  12.0  12.0
1  0.0  -4.0  -2.0
2  0.0   0.0  -3.0
Solution
     0
0  3.0
1  1.0
2 -1.0
------------------
Task3
LU decomposition:
Lower:
     0    1  2
0  1.0  0.0  0
1  4.0  1.0  0
2  7.0  2.0  1
Upper:
     0    1    2
0  1.0  2.0  3.0
1  0.0 -3.0 -6.0
2  0.0  0.0  0.0
Impossible to carry out backward substitution because element is too small for division!
------------------
Task4
LU decomposition:
Lower:
              0    1  2
0  1.000000e+00  0.0  0
1  1.000000e+12  1.0  0
2  2.000000e+12  2.0  1
Upper:
          0             1             2
0  0.000001  3.000000e+06  2.000000e+06
1  0.000000 -3.000000e+18 -2.000000e+18
2  0.000000  0.000000e+00 -2.000896e+06
Solution
          0
0  1.000240
1  1.999318
2  3.001024
LUP decomposition:
Lower:
              0    1  2
0  1.000000e+00  0.0  0
1  5.000000e-13  1.0  0
2  5.000000e-01  0.5  1
Upper:
           0             1             2
0  2000000.0  1.000000e+06  2.000000e+06
1        0.0  3.000000e+06  2.000000e+06
2        0.0  0.000000e+00  1.000000e+06
Solution
     0
0  1.0
1  2.0
2  3.0
------------------
Task5
LUP decomposition:
Lower:
          0    1  2
0  1.000000  0.0  0
1  0.666667  1.0  0
2  0.000000 -0.3  1
Upper:
     0         1         2
0  3.0  5.000000  1.000000
1  0.0 -3.333333  2.333333
2  0.0  0.000000  2.700000
Solution
              0
0 -1.036208e-15
1  5.329071e-16
2  3.000000e+00
------------------
Task6
LUP decomposition:
Lower:
              0             1  2
0  1.000000e+00  0.000000e+00  0
1  1.000000e-09  1.000000e+00  0
2  7.500000e-20  4.250000e-10  1
Upper:
              0             1             2
0  4.000000e+09  1.000000e+09  3.000000e+09
1  0.000000e+00  1.000000e+00  4.000000e+00
2  0.000000e+00  0.000000e+00 -1.725000e-09
Impossible to carry out backward substitution because element is too small for division!
------------------
Task7
Matrix inverse:
Impossible to carry out backward substitution because element is too small for division!
------------------
Task8
Matrix inverse:
     0    1    2
0 -0.0 -3.0 -2.0
1  1.0 -4.0 -2.0
2 -3.0  4.0  1.0
------------------
Task9
Matrix determinant:
1.0
------------------
Task10
Matrix determinant:
48.0