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Nuevas matrices

1. Si una matriz que tiene una línea de ceros,
     su determinante es cero.

3. Si en una matriz  una línea es combinación 
     lineal de otras, su determinante es cero.

2.  El determinante de una matriz que tiene dos
      líneas proporcionales, es cero.

5. Si permutamos dos líneas, el determinante cambia de signo.

 C_{1} ↔ C_{2} 

6. Si en una matriz multiplicamos una línea por un número,
    el determinante queda multiplicado por ese número.

 \left| M \right| =\left| M^{t} \right| 

  \left| A·B \right| =\left| A  \right| ·\left| B \right| 

9. Suma de determinantes con todas las líneas iguales excepto una.

10. El determinante de una matriz triangular es igual
al producto de los elementos de la diagonal principal.

Todos los sumandos tienen un cero como factor
excepto el primero (el de la diagonal principal).

Cada sumando tiene un cero como factor.

4. Si a una línea se le suma una combinación lineal
de otras, el determinante no varía.

7. El determinante de una matriz y el de su traspuesta coinciden.

8. El determinante del producto de dos matrices
es igual al producto de los determinantes.

C8 = Random(-9, 9)
G17 = Random(2, 4)
A17 = Random(-9, 9)
G11 = Random(2, 4)
B11 = Random(-9, 9)
A11 = Random(-9, 9)
C7 = Random(-9, 9)
A1 = Random(-9, 9)
B8 = Random(-9, 9)
B7 = Random(-9, 9)
E8 = Random(2, 4)
E7 = Random(2, 4)
A8 = Random(-9, 9)
D4 = Random(2, 4)
A7 = Random(-9, 9)
A4 = Random(-9, 9)
A2 = Random(-9, 9)
B1 = 0 (slider from -5 to 5, step 1)
B2: 0
B4 = Random(-9, 9)
A5: (A4 * D4)
B5: (B4 * D4)
A9: (A7 * E7) - (A8 * E8)
C9: (C7 * E7) - (C8 * E8)
B9: (B7 * E7) - (B8 * E8)
A12 = Random(-9, 9)
B12 = Random(-9, 9)
D12: A12 + (G11 * B12)
D11: A11 + (G11 * B11)
E11: B11
E12: B12
A14 = Random(-9, 9)
A15 = Random(-9, 9)
B14 = Random(-9, 9)
B15 = Random(-9, 9)
D14: B14
D15: B15
E14: A14
E15: A15
B17 = Random(-9, 9)
A18 = Random(-9, 9)
B18 = Random(-9, 9)
D18: A18
D17: (G17 * A17)
E17: (G17 * B17)
E18: B18
A20 = Random(-9, 9)
B20 = Random(-9, 9)
A21 = Random(-9, 9)
B21 = Random(-9, 9)
D20: A20
D21: B20
E20: A21
E21: B21
A23 = Random(-9, 9)
B23 = Random(-9, 9)
A24 = Random(-9, 9)
B24 = Random(-9, 9)
D23 = Random(-9, 9)
E23 = Random(-9, 9)
D24 = Random(-9, 9)
E24 = Random(-9, 9)
G23: (A23 * D23) + (B23 * D24)
H23: (A23 * E23) + (B23 * E24)
G24: (A24 * D23) + (B24 * D24)
H24: (A24 * E23) + (B24 * E24)
A26 = Random(-9, 9)
B26 = Random(-9, 9)
A27 = Random(-9, 9)
B27 = Random(-9, 9)
D26 = Random(-9, 9)
D27 = Random(-9, 9)
E26: B26
E27: B27
G26: A26 + D26
H26: B26
G27: A27 + D27
H27: B27
A29 = Random(-9, 9)
B29 = Random(-9, 9)
C29 = Random(-9, 9)
B30 = Random(-9, 9)
C30 = Random(-9, 9)
C31 = Random(-9, 9)
A30: 0
A31: 0
B31: 0
I1 = Sequence(i, i, 1, 10)
i = SelectedIndex(I1)
m1: {{A1, B1}, {A2, B2}}
m2: {{A4, B4}, {A5, B5}}
m3: {{A7, B7, C7}, {A8, B8, C8}, {A9, B9, C9}}
m41: {{A11, B11}, {A12, B12}}
m42: {{D11, E11}, {D12, E12}}
m51: {{A14, B14}, {A15, B15}}
m52: {{D14, E14}, {D15, E15}}
m61: {{A17, B17}, {A18, B18}}
m62: {{D17, E17}, {D18, E18}}
m71: {{A20, B20}, {A21, B21}}
m81: {{A23, B23}, {A24, B24}}
m82: {{D23, E23}, {D24, E24}}
m83: {{G23, H23}, {G24, H24}}
m91: {{A26, B26}, {A27, B27}}
m92: {{D26, E26}, {D27, E27}}
m93: {{G26, H26}, {G27, H27}}
ma1: {{A29, B29, C29}, {A30, B30, C30}, {A31, B31, C31}}
d1 = Determinant(m1)
texto1: "\left|" + (LaTeX[m1]) + "  \right| =\left( " + (LaTeX[A1]) + "  \right) ·\left(  " + (LaTeX[B2]) + " \right) -\left(" + (LaTeX[A2]) + "   \right)·\left(  " + (LaTeX[B1]) + " \right) =" + (LaTeX[d1]) + " "
d2 = Determinant(m2)
texto4: "\left| " + (LaTeX[m2]) + "  \right| =\left(   " + (LaTeX[A4]) + " \right) ·\left(  " + (LaTeX[B5]) + "  \right) -\left(  " + (LaTeX[A5]) + "  \right)·\left(  " + (LaTeX[B4]) + "  \right) =  " + (LaTeX[d2]) + ""
d3 = Determinant(m3)
d41 = Determinant(m41)
d42 = Determinant(m42)
d51 = Determinant(m51)
d52 = Determinant(m52)
d61 = Determinant(m61)
d62 = Determinant(m62)
d71 = Determinant(m71)
d81 = Determinant(m81)
d82 = Determinant(m82)
d83 = Determinant(m83)
d91 = Determinant(m91)
d92 = Determinant(m92)
d93 = Determinant(m93)
da1 = Determinant(ma1)
texto7: "\left|   " + (LaTeX[m3]) + "  \right| ="
texto9: " F_{3}= " + (LaTeX[E7]) + "·F_{1}-" + (LaTeX[E8]) + "·F_{2}"
texto12: "\left| " + (LaTeX[m41]) + "  \right| =\left(  " + (LaTeX[A11]) + "  \right) ·\left(  " + (LaTeX[B12]) + "  \right) -\left(  " + (LaTeX[A12]) + "  \right)·\left( " + (LaTeX[B11]) + "   \right) =  " + (LaTeX[d41]) + ""
texto3: " F_{2} = " + (LaTeX[D4]) + " · F_{1}"
B = (-1, 2)
texto13: "\left|  " + (LaTeX[m42]) + " \right| =\left(  " + (LaTeX[D11]) + "  \right) ·\left(  " + (LaTeX[E12]) + "  \right) -\left(  " + (LaTeX[D12]) + "  \right)·\left( " + (LaTeX[E11]) + "   \right) = " + (LaTeX[d42]) + ""
texto16: "\left|  " + (LaTeX[m51]) + "  \right| =\left(  " + (LaTeX[A14]) + "   \right) ·\left(   " + (LaTeX[B15]) + "  \right) -\left(  " + (LaTeX[A15]) + "   \right)·\left(  " + (LaTeX[B14]) + "   \right) =   " + (LaTeX[d51]) + ""
texto17: "\left|  " + (LaTeX[m52]) + "  \right| =\left(   " + (LaTeX[D14]) + "  \right) ·\left(  " + (LaTeX[E15]) + "   \right) -\left(   " + (LaTeX[D15]) + "  \right)·\left( " + (LaTeX[E14]) + "    \right) =   " + (LaTeX[d52]) + ""
texto20: "\left|  " + (LaTeX[m61]) + "  \right| =\left(  " + (LaTeX[A17]) + "   \right) ·\left(   " + (LaTeX[B18]) + "  \right) -\left( " + (LaTeX[A18]) + "    \right)·\left(  " + (LaTeX[B17]) + "   \right) =  " + (LaTeX[d61]) + " "
texto21: "\left|  " + (LaTeX[m62]) + "  \right| =\left(  " + (LaTeX[D17]) + "   \right) ·\left(   " + (LaTeX[E18]) + "  \right) -\left(  " + (LaTeX[D18]) + "   \right)·\left(  " + (LaTeX[E17]) + "   \right) =   " + (LaTeX[d62]) + ""
m72: {{D20, E20}, {D21, E21}}
d72 = Determinant(m72)
texto26: "\left| A \right| =\left| " + (LaTeX[m81]) + "    \right| =\left(   " + (LaTeX[A23]) + "    \right) ·\left(    " + (LaTeX[B24]) + "   \right) -\left(  " + (LaTeX[A24]) + "     \right)·\left(   " + (LaTeX[B23]) + "    \right) =   " + (LaTeX[d81]) + "  "
texto27: "\left| B \right| =\left|  " + (LaTeX[m82]) + "    \right| =\left(  " + (LaTeX[D23]) + "      \right) ·\left(   " + (LaTeX[E24]) + "     \right) -\left(     " + (LaTeX[D24]) + "   \right)·\left(   " + (LaTeX[E23]) + "     \right) =    " + (LaTeX[d82]) + "  "
texto28: "\left| A·B \right| =\left|  " + (LaTeX[m83]) + "    \right| =\left(     " + (LaTeX[G23]) + "   \right) ·\left(   " + (LaTeX[H24]) + "     \right) -\left(    " + (LaTeX[G24]) + "    \right)·\left(  " + (LaTeX[H23]) + "      \right) =      " + (LaTeX[d83]) + ""
texto23: "\left|  M\right|= \left|  " + (LaTeX[m71]) + "  \right| =\left(  " + (LaTeX[A20]) + "    \right) ·\left(  " + (LaTeX[B21]) + "    \right) -\left(   " + (LaTeX[A21]) + "   \right)·\left(    " + (LaTeX[B20]) + "  \right) =    " + (LaTeX[d71]) + ""
texto24: "\left| M^{t} \right| =\left|  " + (LaTeX[m72]) + "   \right| =\left(  " + (LaTeX[D20]) + "    \right) ·\left(    " + (LaTeX[E21]) + "  \right) -\left(  " + (LaTeX[D21]) + "    \right)·\left(  " + (LaTeX[E20]) + "    \right) =    " + (LaTeX[d72]) + ""
texto30: "\left| " + (LaTeX[m91]) + "     \right| +\left|   " + (LaTeX[m92]) + "    \right| =\left|   " + (LaTeX[m93]) + "    \right| "
texto31: "\left|   " + (LaTeX[m91]) + "   \right| =\left( " + (LaTeX[A26]) + "       \right) ·\left(   " + (LaTeX[B27]) + "     \right) -\left(   " + (LaTeX[A27]) + "     \right)·\left(   " + (LaTeX[B26]) + "     \right) =      " + (LaTeX[d91]) + ""
texto32: "\left|   " + (LaTeX[m92]) + "   \right| =\left(  " + (LaTeX[D26]) + "   \right) ·\left(     " + (LaTeX[E27]) + "   \right) -\left(  " + (LaTeX[D27]) + "      \right)·\left(     " + (LaTeX[E26]) + "   \right) =     " + (LaTeX[d92]) + " "
texto33: "\left|  " + (LaTeX[m93]) + "    \right| =\left(   " + (LaTeX[G26]) + "     \right) ·\left(  " + (LaTeX[H27]) + "      \right) -\left(     " + (LaTeX[G27]) + "   \right)·\left(   " + (LaTeX[H26]) + "     \right) =      " + (LaTeX[d93]) + ""
texto35: "\left|   " + (LaTeX[ma1]) + "   \right| ="
texto39: "Propiedad " + i + ""
texto19: " F_{1}^{'} = " + (LaTeX[G17]) + " · F_{1} "
texto11: " C_{1}^{'} = C_{1} + " + (LaTeX[G11]) + " · C_{2}"
texto42: "-\left(  " + (LaTeX[A9]) + "    \right) ·\left(   " + (LaTeX[B8]) + "   \right)  ·\left(   " + (LaTeX[C7]) + "   \right) -\left(   " + (LaTeX[B7]) + "  \right) ·\left( " + (LaTeX[A8]) + "   \right)  ·\left(   " + (LaTeX[C9]) + "   \right)  -\left(   " + (LaTeX[A7]) + "   \right) ·\left(  " + (LaTeX[B9]) + "   \right)  ·\left(   " + (LaTeX[C8]) + "   \right)= " + (LaTeX[d3]) + ""
texto6: "=\left(  " + (LaTeX[A7]) + "   \right) ·\left(  " + (LaTeX[B8]) + "   \right)  ·\left( " + (LaTeX[C9]) + "    \right) +\left(   " + (LaTeX[A8]) + "  \right) ·\left( " + (LaTeX[B9]) + "    \right)  ·\left(  " + (LaTeX[C7]) + "   \right) +\left(  " + (LaTeX[A9]) + "   \right) ·\left(  " + (LaTeX[C8]) + "   \right)  ·\left(  " + (LaTeX[B7]) + "   \right)- "
texto43: "-\left(  " + (LaTeX[A31]) + "     \right) ·\left(   " + (LaTeX[B30]) + "    \right)  ·\left(    " + (LaTeX[C29]) + "   \right) -\left(    " + (LaTeX[A29]) + "  \right) ·\left(  " + (LaTeX[B31]) + "   \right)  ·\left(   " + (LaTeX[C30]) + "    \right)  -\left(   " + (LaTeX[B29]) + "    \right) ·\left(     " + (LaTeX[A30]) + " \right)  ·\left(   " + (LaTeX[C31]) + "    \right)= " + (LaTeX[da1]) + " "
texto36: "=\left(  " + (LaTeX[A29]) + "    \right) ·\left(  " + (LaTeX[B30]) + "    \right)  ·\left(   " + (LaTeX[C31]) + "   \right) +\left(  " + (LaTeX[A30]) + "    \right) ·\left(   " + (LaTeX[B31]) + "   \right)  ·\left(   " + (LaTeX[C29]) + "   \right) +\left(    " + (LaTeX[A31]) + "  \right) ·\left(  " + (LaTeX[C30]) + "    \right)  ·\left(  " + (LaTeX[B29]) + "    \right) -"
texto44: "\left| A \right|·\left| B \right| =" + (LaTeX[d81]) + "·\left( " + (LaTeX[d82]) + "  \right) =" + (LaTeX[d83]) + ""