The document describes solving a system of linear equations using Gauss-Jordan elimination. It provides the steps to row reduce the coefficient matrix: 1) Perform row operations to transform the matrix into reduced row echelon form. 2) Read the solutions for X, Y, and W directly from the reduced matrix. 3) Substitute the solutions back into the original equation to solve for F(t).

1. Método de Gauss Jordan
X + 2Y - W = -1
-2X + 2Y – 6W = 2
X + Y + W = 4
GAUSS JORDAN
PARA CÉDULAS QUE
TERMINEN EN 6, 7, 8 Y 9
F(t) = 2Y” + Z4” – 3X2 ´
1 2 -1 -1
-2 2 -6 2
1 1 1 4
① 2R₃ + R₂ → R₃
1 2 -1 -1
-2 2 -6 2
0 4 -4 10
② 2R₁ + R₂ → R₂
1 2 -1 -1
0 6 -8 0
0 4 -4 10
③ -6R₃ + 4R₂ → R₃
1 2 -1 -1
0 6 -8 0
0 0 -8 -60
④ R₃ / (-8) → R₃
1 2 -1 -1
0 6 -8 0
0 0 1 7,5
⑤ R₃ + R₁ → R₁
1 2 0 6,5
0 6 -8 0
0 0 1 7,5
⑥ 8R₃ + R₂ → R₂
1 2 0 6,5
0 6 0 60
0 0 1 7,5
⑦ -3R₁ + R₂ → R₁
-3 0 0 40,5
0 6 0 60
0 0 1 7,5
⑧ R₁ / (-3) → R₁
1 0 0 -13,5
0 6 0 60
0 0 1 7,5
⑨ R₂ / 6 → R₂
1 0 0 -13,5
0 1 0 10
0 0 1 7,5
X = -13,5
Y = 10
W = 7,5
F(t) = 2Y’’ + Z4’’ – 3X2’
F(t) = 2(10)’’ + 1⁴’’ -3(-13,5)²
F(t) = 20’’ +1⁴’’ -6(-13,5)
F(t) = 20’’ + 1⁴’’ +81
F(t) = 20’’ + 0 + 81
F(t) = 1 + 0 + 81