Perform the Gauss elimination with the scaled partial pivoti

Perform the Gauss elimination with the scaled partial pivoting for the following matrix A. Show the contents of A (mark multipliers) and of the permutation array in all intermediate steps. Finally, write down the corresponding L and U matrices.

Solution

2 4 4 2
3 3 3 3
1 5 0 1
1 2 3 4

Interchange 4th and I row

1 2 3 4

2 4 4 2
3 3 3 3
1 5 0 1

Continuing in this way

Lower =

1   0   0   0  
0.333   1   0   0  
0.333   0.25   1   0  
0.667   0.5   1.111   1  

Upper

3   3   3   3  
0   4   -1   0  
0   0   2.25   3  
0   0   0   -3.333

Permutation matrix =

0   1   0   0  
0   0   1   0  
0   0   0   1  
1   0   0   0     

1	2	3	4
2	4	4	2
3	3	3	3
1	5	0	1
C2 = C2-2C1, C3 = C3-3C3, C4=C4-4C4
1	0	0	0
2	0	-2	-6
3	-3	-6	-9
1	3	-3	-3
C3/3 =C3
1	0	0	0
2	0	-2	-6
3	-1	-6	-9
1	1	-3	-3