Hola

Gauss Jordan

.....1....-2....1.....1.....0.....0

.....3.....2....3.....0.....1.....0

.....2....-3....-3.....0.....0.....1

F2 =F2 - 3 F1

F3 = F3 - 2 F1

.....1....-2....1.....1.....0.....0

.....0.....8....0....-3.....1.....0

.....0....1....-5....-2.....0.....1

F2 = F2 - 8*F3

F3<->F2

.....1...-2....1.....1.....0.....0

.....0....1...-5....-2.....0.....1

.....0....0...40...13.....1....-8

F3 = F3 * (1/40)

.....1...-2....1.....1......0......0

.....0....1...-5....-2......0......1

.....0....0...1..13/40.1/40.-1/5

F2 = F2 + 5 * F3

.....1..-2....1.....1......0......0

.....0....1...0..-3/8...1/8......0

.....0....0...1..13/40.1/40.-1/5

F1 = F1 + 2 F2 - F3

.....1....0...0...-3/40...9/40...1/5

.....0....1...0....-3/8....1/8.....0

.....0....0...1...13/40..1/40..-1/5

Matri inversa

A^-1 =

......-3/40...9/40....1/5

.......-3/8......1/8......0

......13/40...1/40....-1/5

ó

A^-1 =

......-3/40...9/40....8/40

....-15/40...5/40......0

.....13/40...1/40....-8/40

B =

...3..

..-3..

..-5..

X = A^-1 * B =

....(-3*(3)+9*(-3)+8*(-5))/40..

....(-15*(3)+5*(-3)+0*(-5))/40..

....(13*(3)+1*(-3)-8*(-5))/40..

X = A^-1 * B =

...-76/40

...-60/40

....76/40

***************************

X = A^-1 * B =

..-1.9

..-1.5

...1.9

***************************

Metodo de Cramer

D = Det

.....1....-2....1

.....3.....2....3

.....2....-3...-3

D = -40

***********

D * x = Det

.....5....-2....1

....-3.....2....3

....-3....-3...-3

x = 76/-40

x = -1.9

************

D * y = Det

.....1....5....1

.....3...-3....3

.....2...-3...-3

y = 60/-40

y = -1.5

**************

D * z = Det

.....1....-2...5

.....3.....2..-3

.....2....-3..-3

x = -76/-40

x = 1.9

************