# Factorization of sample matrix

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NA on 8 Mar 2022
Edited: NA on 8 Mar 2022
I have T matrix
T = [-1 -1 -1 -1 -1 1 0 0;
0 2 0 0 0 0 0 0;
0 0 3 0 0 0 0 0;
0 -1 -1 -1 -1 0 1 0;
0 0 0 0 5 6 0 0;
0 0 0 0 0 6 0 0;
0 -1 -1 -1 0 0 0 1;
0 2 3 0 0 0 0 0];
How can I determine this factorization?
T=[L;M][U]
L and U are square lower and upper triangular matrices
M is a rectangular matrix.
The factorization of T yields one zero pivot at row/column 8.
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NA on 8 Mar 2022
The factorization of T yields one zero pivot at row/column 8.
This zero pivot is replaced by 1 and the following modified factors are obtained:
L = [ 1 0 0 0 0 0 0 0;
0 1 0 0 0 0 0 0;
0 0 1 0 0 0 0 0;
-1 -1 0 1 0 0 0 0;
0 0 0 0 1 0 0 0;
0 -1 0 1 0 1 0 0;
0 -1 0 1 1 1 1 0;
0 1 -1 0 0 0 0 1];
U = [ 1 0 0 0 0 1 0 0;
0 1 1 0 0 0 0 0;
0 0 1 0 0 0 0 0;
0 0 0 -1 -1 2 0 0;
0 0 0 0 1 0 0 0;
0 0 0 0 0 -2 1 0;
0 0 0 0 0 0 -1 1;
0 0 0 0 0 0 0 1];
I do not understand how I can find pivot and replace it by 1?