a_{12}

a_{13}

a_{21}

a_{22}

a_{23}

a_{31}

a_{32}

a_{33}

a_{14}

a_{24}

a_{11}

¿Primera fila?

Ceros \;  en \;  1^{a} \;  columna

Comenzar

SI

NO

SI

NO

¿Cambia orden de filas?

SI

NO

SI

NO

Coeficientes del sistema

Ecuaciones

Si \;  a_{2,2}≟ 0 \;  intercambia \;  F_{2} \; con  \; F_{3}

Hacer \; a_{2,2}=1

SI

NO

Intercambia F_{2} con F_{3}

¿ a_{3,3}≟ 0?

SI

NO

La matriz no tiene inversa

Hacer \; a_{3,3}=1

Ceros \;  en \;  2^{a} \;  columna

Introduce los elementos de la matriz

La matriz 

 a_{1,1} =1

Ceros \;  en \;  la  \; primera \;  columna

Intercambia fila 2 con fila 3

 a_{2,2} =1

Ceros \;  en \;  la  \; segunda \;  columna

a_{11} ≠0

Intercambia filas

La matriz no tiene inversa

a14

a24

a34

a_{34}

Coloca los valores de a, b, c y d 
para hacer los ceros en 1ª columna

Coloca los valores de e y f para hacer los ceros en 2ª columna

Ver solución

Ocultar solución

f = -7 (slider from B22 to B21, step 1)
e = 11 (slider from B22 to B21, step 1)
B3 = -2
B2 = 4
B1 = 3
a = 5 (slider from A13 to A12, step 1)
b = 3 (slider from A13 to A12, step 1)
A3 = -1
A2 = 3
A1 = 5
B5 = If($A$1 ≠ 0, B1, If[$A$2 ≠ 0, B2, B3])
B14: B5
B7 = If($A$1 ≟ 0 ∧ $A$2 ≟ 0 ∧ ($A$3 ≠ 0), B1, B3)
B11: B7
B16: B11
B6 = If($A$1 ≟ 0 ∧ ($A$2 ≠ 0), B1, B2)
B10: B6
B15: B10
B19: (B15 * a) - (B14 * b)
c = 5 (slider from A13 to A12, step 1)
d = -1 (slider from A13 to A12, step 1)
B20: (B16 * c) - (B14 * d)
A7 = If($A$1 ≟ 0 ∧ $A$2 ≟ 0 ∧ ($A$3 ≠ 0), A1, A3)
A11: A7
A16: A11
A5 = If($A$1 ≠ 0, A1, If[$A$2 ≠ 0, A2, A3])
A14: A5
A6 = If($A$1 ≟ 0 ∧ ($A$2 ≠ 0), A1, A2)
A10: A6
A15: A10
F1 = 0 (slider from -5 to 5, step 1)
F2 = 0
F6 = If($A$1 ≟ 0 ∧ ($A$2 ≠ 0), F1, F2)
F3 = 1
F7 = If($A$1 ≟ 0 ∧ $A$2 ≟ 0 ∧ ($A$3 ≠ 0), F1, F3)
F5 = If($A$1 ≠ 0, F1, If[$A$2 ≠ 0, F2, F3])
E1 = 0
E2 = 1
E6 = If($A$1 ≟ 0 ∧ ($A$2 ≠ 0), E1, E2)
E3 = 0
E7 = If($A$1 ≟ 0 ∧ $A$2 ≟ 0 ∧ ($A$3 ≠ 0), E1, E3)
E5 = If($A$1 ≠ 0, E1, If[$A$2 ≠ 0, E2, E3])
D1 = 5
D2 = 7
D6 = If($A$1 ≟ 0 ∧ ($A$2 ≠ 0), D1, D2)
D3 = -3
D7 = If($A$1 ≟ 0 ∧ $A$2 ≟ 0 ∧ ($A$3 ≠ 0), D1, D3)
D5 = If($A$1 ≠ 0, D1, If[$A$2 ≠ 0, D2, D3])
C1 = -1
C2 = -2
C6 = If($A$1 ≟ 0 ∧ ($A$2 ≠ 0), C1, C2)
C3 = 0
C7 = If($A$1 ≟ 0 ∧ $A$2 ≟ 0 ∧ ($A$3 ≠ 0), C1, C3)
C5 = If($A$1 ≠ 0, C1, If[$A$2 ≠ 0, C2, C3])
A7_1 = NaN
A6_1 = NaN
A5_1 = NaN
n11 = 0 (slider from 0 to 1, step 1)
n = 1 (slider from 1 to 3, step 1)
F9: F5
A9: A5
E9: E5
D9: D5
C9: C5
B9: B5
F14 = If(n11 ≟ 0, F9, F9 / $A9)
F18: F14
F23: F18
F10: F6
F15: F10
F11: F7
F16: F11
F20: F16 - (F14 * $A$16)
F19: F15 - (F14 * $A$15)
F24 = If($B$19 ≟ 0, F20, F19)
B24 = If($B$19 ≟ 0, B20, B19)
F25 = If($B$19 ≟ 0, F19, F20)
E14 = If(n11 ≟ 0, E9, E9 / $A9)
E18: E14
E23: E18
E10: E6
E15: E10
E11: E7
E16: E11
E20: (E16 * c) - (E14 * d)
E19: E15 - (E14 * $A$15)
E24 = If($B$19 ≟ 0, E20, E19)
E25 = If($B$19 ≟ 0, E19, E20)
D14: D5
D18: D14
D10: D6
D23: D18
D11: D7
D15: D10
D16: D11
D20: (D16 * c) - (D14 * d)
D19: (D15 * a) - (D14 * b)
D24 = If($B$19 ≟ 0, D20, D19)
D25 = If($B$19 ≟ 0, D19, D20)
C14: C5
C18: C14
C10: C6
C23: C18
C11: C7
C15: C10
C16: C11
C20: (C16 * c) - (C14 * d)
C19: (C15 * a) - (C14 * b)
C24 = If($B$19 ≟ 0, C20, C19)
C25 = If($B$19 ≟ 0, C19, C20)
B18: B14
B23: B18
A19: (A15 * a) - (A14 * b)
A20: (A16 * c) - (A14 * d)
B25 = If($B$19 ≟ 0, B19, B20)
A25 = If($B$19 ≟ 0, A19, A20)
A24 = If($B$19 ≟ 0, A20, A19)
A18: A14
A23: A18
B27: B23
B29: (B20 * e) - (B19 * f)
B28: B19
C29: (C20 * f) - (C19 * e)
D29: (D20 * f) - (D19 * e)
E29: E25
F29: F25
A29: (A20 * f) - (A19 * e)
C28: C19
D28: D19
E28: E24 / $B$24
F28: F24 / $B$24
A28: A19
C27: C23
D27: D23
E27: E23
F27: F23
A27: A23
B31: B23
A31: A23
C31: C23
D31: D23
F31: F27 - (F28 * $B$27)
E31: E23
B12 = 2
C32: C28
B32: B28
D32: D28
A32: A28
F32: F28
E32: E28
C12 = 1
C33: C29 - (C28 * $B$29)
D33: D29 - (D28 * $B$29)
D12 = 3
A33: A29 - (A28 * $B$29)
B33: B29 - (B28 * $B$29)
F33: F29 - (F28 * $B$29)
E33: E29 - (E28 * $B$29)
CasillaDeEntrada12 = Textfield(B1)
CasillaDeEntrada13 = Textfield(C1)
CasillaDeEntrada21 = Textfield(A2)
CasillaDeEntrada22 = Textfield(B2)
CasillaDeEntrada23 = Textfield(C2)
CasillaDeEntrada31 = Textfield(A3)
CasillaDeEntrada32 = Textfield(B3)
CasillaDeEntrada33 = Textfield(C3)
CasillaDeEntrada14 = Textfield(D1)
CasillaDeEntrada24 = Textfield(D2)
CasillaDeEntrada11 = Textfield(A1)
texto5b: "( " + A18 + " ) x + ( " + B18 + " ) y + ( " + C18 + " ) z = " + D18 + "
( " + A19 + " ) x + ( " + B19 + " ) y + ( " + C19 + " ) z = " + D19 + "
( " + A20 + " ) x + ( " + B20 + " ) y + ( " + C20 + " ) z = " + D20 + ""
texto5: "( " + A1 + " ) x + ( " + B1 + " ) y + ( " + C1 + " ) z = " + D1 + "
( " + A2 + " ) x + ( " + B2 + " ) y + ( " + C2 + " ) z = " + D2 + "
( " + A3 + " ) x + ( " + B3 + " ) y + ( " + C3 + " ) z = " + D3 + ""
texto5c: "( " + A31 + " ) x + ( " + B31 + " ) y + ( " + C31 + " ) z = " + D31 + "
( " + A32 + " ) x + ( " + B32 + " ) y + ( " + C32 + " ) z = " + D32 + "
( " + A33 + " ) x + ( " + B33 + " ) y + ( " + C33 + " ) z = " + D33 + ""
B22: Min[B19:B20] - 2
CasillaDeEntradat5 = Textfield(B22)
A45: D33 / C33
A44: (D32 - (A45 * C32)) / B32
A43: (D31 - (C31 * A45) - (B31 * A44)) / A31
texto5a: "( " + (LaTeX[A9]) + " ) x + ( " + (LaTeX[B9]) + " ) y + ( " + (LaTeX[C9]) + " ) z = " + (LaTeX[D9]) + "
( " + (LaTeX[A10]) + " ) x + ( " + (LaTeX[B10]) + " ) y + ( " + (LaTeX[C10]) + " ) z = " + (LaTeX[D10]) + "
( " + (LaTeX[A11]) + " ) x + ( " + (LaTeX[B11]) + " ) y + ( " + (LaTeX[C11]) + " ) z = " + (LaTeX[D11]) + ""
i = 1 (slider from 0 to 1, step 1)
j = 1 (slider from 0 to 1, step 1)
k = 1 (slider from 0 to 1, step 1)
n1 = 0 (slider from 0 to 1, step 1)
n2 = 0 (slider from 0 to 1, step 1)
n3 = 0 (slider from 0 to 1, step 1)
n4 = 0 (slider from 0 to 1, step 1)
A: {{A1, B1, C1, D1}, {A2, B2, C2, D2}, {A3, B3, C3, D3}}
B: {{A9, B9, C9, D9}, {A10, B10, C10, D10}, {A11, B11, C11, D11}}
D: {{A18, B18, C18, D18}, {A19, B19, C19, D19}, {A20, B20, C20, D20}}
G: {{A31, B31, C31, D31}, {A32, B32, C32, D32}, {A33, B33, C33, D33}}
textoma: "A=" + (LaTeX[A]) + ""
texto5e: "( " + (LaTeX[B32]) + " ) y + ( " + (LaTeX[C32]) + " ) · ( " + (LaTeX[A45]) + " ) = " + (LaTeX[D32]) + " \;  \;  ;\;  \;  y = " + (LaTeX[A44]) + ""
texto5f: "( " + (LaTeX[A31]) + " ) x + ( " + (LaTeX[B31]) + " ) · ( " + (LaTeX[A44]) + " ) + ( " + (LaTeX[C31]) + " ) · ( " + (LaTeX[A45]) + " ) = " + (LaTeX[D31]) + " \;  \; ;\;  \; x = " + (LaTeX[A43]) + ""
E12 = 3
F12 = 3
C: {{A14, B14, C14, D14}, {A15, B15, C15, D15}, {A16, B16, C16, D16}}
textomc: "" + (LaTeX[C]) + ""
textoa = If(B19 ≟ 0, textoa1, textoa2)
F: {{A27, B27, C27, D27}, {A28, B28, C28, D28}, {A29, B29, C29, D29}}
texto3g: "F_{3}=F_{3}-(" + (LaTeX[B29]) + " ) ·F_{2}"
textob = If(C33 ≟ 0, textob1, textob2)
A35: A31
A37: A33 / $C$33
A36: A32
B35: B31
B37: B33 / $C$33
B36: B32
C35: C31
C37: C33 / $C$33
C36: C32
D35: D31
D37: D33 / $C$33
D36: D32
E35: E31
E37: E33 / $C$33
E36: E32
F35: F31
F37: F33 / $C$33
F36: F32
A41: A37
B41: B37
C41: C37
D41: D37
E41: E37
F41: F37
G37 = NaN
G36 = NaN
G35 = NaN
H37 = NaN
H36 = NaN
H35 = NaN
A39: A35 - (A37 * $C$35)
B39: B35 - (B37 * $C$35)
C39: C35 - (C37 * $C$35)
D39: D35 - (D37 * $C$35)
E39: E35 - (E37 * $C$35)
F39: F35 - (F37 * $C$35)
A40: A36 - (A37 * $C$36)
B40: B36 - (B37 * $C$36)
C40: C36 - (C37 * $C$36)
D40: D36 - (D37 * $C$36)
E40: E36 - (E37 * $C$36)
F40: F36 - (F37 * $C$36)
J: {{D39, E39, F39}, {D40, E40, F40}, {D41, E41, F41}}
textomb: "" + (LaTeX[B]) + ""
textomd: "" + (LaTeX[D]) + ""
textomf: "" + (LaTeX[F]) + ""
textomg: "" + (LaTeX[G]) + ""
E_1 = (-1.5728530913216108, 1.5467385138967662)
K = (-1.5528871242200795, -2.4264889393079967)
n5 = 0 (slider from 0 to 1, step 1)
E: {{A23, B23, C23, D23}, {A24, B24, C24, D24}, {A25, B25, C25, D25}}
textome: "" + (LaTeX[E]) + ""
lista1: {A5, B5, C5, D5, E5, F5, A6, B6, C6, D6, E6, F6, A7, B7, C7, D7, E7, F7}
AA: {{A5, B5, C5, D5}, {A6, B6, C6, D6}, {A7, B7, C7, D7}}
textomb1: "" + (LaTeX[AA]) + ""
rg = MatrixRank(A)
CasillaDeEntradax1 = Textfield(D1)
CasillaDeEntradax2 = Textfield(D2)
CasillaDeEntradax3 = Textfield(D3)
A13: Min[A9:A11] - 2
H: {{A35, B35, C35, D35}, {A36, B36, C36, D36}, {A37, B37, C37, D37}}
A12: Max[A9:A11] + 2
I: {{A39, B39, C39, D39}, {A40, B40, C40, D40}, {A41, B41, C41, D41}}
B21: Max[B19:B20] + 2
texto10: "Rango (A)=" + (LaTeX[rg]) + ""
pp = If(A25 ≟ 0 ∧ B25 ≟ 0, 0, 1)
CasillaDeEntrada34 = Textfield(D3)
texto3b: "F_{3}=c· F_{3}-d ·F_{1}=F_{3}=\left( " + (LaTeX[c]) + "  \right) F_{3}-\left(  " + (LaTeX[d]) + " \right)  ·F_{1}"
texto3f: "F_{3}=e·F_{3}-f ·F_{2}=\left(" + (LaTeX[e]) + "  \right) ·F_{1}-\left( " + (LaTeX[f]) + "  \right)·F_{2}"
ll = 0 (slider from 0 to 1, step 1)
texto3a: "F_{2}= a ·F_{2}-b·F_{1}=\left(  " + (LaTeX[a]) + " \right)  F_{2}-\left(   " + (LaTeX[b]) + "\right) ·F_{1}"