Detrminantes

Resolver: |■(6&-5&1@2&4&3@3&2&4)|=6X+2

Se Resuelve el determinante:

|■(6&-5&1@2&4&3@3&2&4)| |█(■(6&-5&1@2&4&3@3&2&4)@■(6&-5&1@2&4&3))|=6.4.4+2.2.1+3.(-5).3-3.4.1-6.2.3-2.(-5).4=

96+4-45-12-36+40=39

Se sustituye el valor del detrminante:

39=6X+2 39-2=6X 37=6X X=37/6

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Hallar: X, Y, Z

|■(-5X&+Y&-3Z@X&-Y&+Z@-3X&+2Y&-Z)■(=@=@=)■(1@3@2)| |■(-5X&+Y&-3Y@X&-Y&+Z@-3&+2Y&-Z)|=|■(1@3@2)| |■(-5&1&-3@1&-1&1@-3&2&-1)||■(X@Y@Z)|=|■(1@3@2)|

Se halla el determinante del sistema: (∆)

|■(-5&1&-3@1&-1&1@-3&2&-1)| |█(■(-5&1&-3@1&-1&1@-3&2&-1)@■(-5&1&-3@1&-1&1))|

∆=5.-1.-1+1.2.-3+(-3).1.1—(-3).(-1).(-3)-(-5).2.1-[1.1.(-1) ]=

∆=5-6-3+9+10+1=16 ∆=16

Se calcula (x,y,z) x=∆x/∆ y=∆y/∆ z=∆z/∆

Cálculo de x:

∆x=|█(■(1&1&-3@3&-1&1@2&2&-1)@■(1&1&-3@3&-1&1))|=1-18+2-6-2+3=-20 ∆x=-20

x=∆x/∆ =(-20)/16=-5/4=-1,25 x=-1,25

Cálculo de y:

∆y=|█(■(-5&1&-3@1&3&1@3&2&-1)@■(-5&1&-3@1&3&1))|=15-6+3-27+10+1=-4 ∆y=-20

y=∆y/∆ =(-4)/16=-1/4=-0,25 y=-0,25

Cálculo de z:

∆z=|█(■(-5&1&1@1&-1&3@3&2&2)@■(-5&1&1@1&-1&3))|=10+2+9+3+30-2=52 ∆z=52

z=∆z/∆ =52/16=26/8=3,25 y=3,25

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