The document describes the Metodo de Thomas method for solving systems of linear equations. It involves setting up the equations in a triangular matrix format with coefficients Aij and then solving for the variables Xj. The method results in a lower triangular matrix L with coefficients Lij that can be used to solve for the variables.

1. Metodo de Thomas
B1 C1 X1 R1
A2 B2 C2 X X2 = R2
A3 B3 C3 X3 R3
A4 B4 X4 R4
X5 R5
1.00000 3 X1 5
3 1.00000 2 X X2 = 11
2 1.00000 5 X3 9
5 1.00000 3 X4 20
3 1 X5 6
1 U11 U12
L21 1 X U22 U23
L32 1 U33 U34
L43 1 U44
L54 1
1 1 3
3 1 -8 2
-0.25 1 X 1.5 5
3.33333 1 -15.667
-0.1915 1
1 D1 R1
L21 1 X D2 = R2
L32 1 D3 R3
L43 1 D4 R4
1 5 5
3 1 X -4 = 11
-0.25 1 8 9
3.33333 1 -6.666667 20
-0.1915 1 4.7234043 6
U11 U12 X1 D1
U22 U23 X X2 = D2
U33 U34 X3 D3

2. U44 X4 D4
1 3 2 5
-8 2 X 1 = -4
1.5 5 2 8
-15.667 3 1 -6.666667
1.5745 3 4.723404

3. A1= 0 B1= 1 C1= 3 R1= 5
A2= 3 B2= 1 C2= 2 R2= 11
A3= 2 B3= 1 C3= 5 R3= 9
A4= 5 B4= 1 C4= 0 R4= 20
A5= 0 B5= 3 C5 0 R5= 6
B1 C1
= A2 B2 C2
A3 B3 C3
u45 A4 B4 C4
u55 a5 b5
1.00000 3
3 1.00000 2
= 2 1.00000 5
3 5 1.00000 3
1.57447 3 1

4. RESPUESTA= 2
1
2
1
3

5. Metodo de cholesky
A11 A12 A13 L11
A21 A22 A23 L21 L22
A31 A32 A33 L31 L32
12 20 12 3.46410162
20 45 25 5.77350269 3.41565026
12 25 40 3.46410162 1.46385011
3.46410162 5.77350269
3.41565026

6. 1
2
L33 4
5.08499192
3.46410162
1.46385011
5.08499192