Matemática discreta Exemplos

Resolva Usando uma Matriz Aumentada 5x-5y+2z=-13 , 10x-10y+4z=-23 , 15x-15y+6z=-37
5x-5y+2z=-135x5y+2z=13 , 10x-10y+4z=-2310x10y+4z=23 , 15x-15y+6z=-3715x15y+6z=37
Etapa 1
Write the system as a matrix.
[5-52-1310-104-2315-156-37]⎢ ⎢5521310104231515637⎥ ⎥
Etapa 2
Encontre a forma escalonada reduzida por linhas.
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Etapa 2.1
Multiply each element of R1R1 by 1515 to make the entry at 1,11,1 a 11.
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Etapa 2.1.1
Multiply each element of R1R1 by 1515 to make the entry at 1,11,1 a 11.
[55-5525-13510-104-2315-156-37]⎢ ⎢ ⎢55552513510104231515637⎥ ⎥ ⎥
Etapa 2.1.2
Simplifique R1R1.
[1-125-13510-104-2315-156-37]⎢ ⎢112513510104231515637⎥ ⎥
[1-125-13510-104-2315-156-37]⎢ ⎢112513510104231515637⎥ ⎥
Etapa 2.2
Perform the row operation R2=R2-10R1 to make the entry at 2,1 a 0.
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Etapa 2.2.1
Perform the row operation R2=R2-10R1 to make the entry at 2,1 a 0.
[1-125-13510-101-10-10-14-10(25)-23-10(-135)15-156-37]
Etapa 2.2.2
Simplifique R2.
[1-125-135000315-156-37]
[1-125-135000315-156-37]
Etapa 2.3
Perform the row operation R3=R3-15R1 to make the entry at 3,1 a 0.
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Etapa 2.3.1
Perform the row operation R3=R3-15R1 to make the entry at 3,1 a 0.
[1-125-135000315-151-15-15-16-15(25)-37-15(-135)]
Etapa 2.3.2
Simplifique R3.
[1-125-13500030002]
[1-125-13500030002]
Etapa 2.4
Multiply each element of R2 by 13 to make the entry at 2,4 a 1.
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Etapa 2.4.1
Multiply each element of R2 by 13 to make the entry at 2,4 a 1.
[1-125-135030303330002]
Etapa 2.4.2
Simplifique R2.
[1-125-13500010002]
[1-125-13500010002]
Etapa 2.5
Perform the row operation R3=R3-2R2 to make the entry at 3,4 a 0.
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Etapa 2.5.1
Perform the row operation R3=R3-2R2 to make the entry at 3,4 a 0.
[1-125-13500010-200-200-202-21]
Etapa 2.5.2
Simplifique R3.
[1-125-13500010000]
[1-125-13500010000]
Etapa 2.6
Perform the row operation R1=R1+135R2 to make the entry at 1,4 a 0.
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Etapa 2.6.1
Perform the row operation R1=R1+135R2 to make the entry at 1,4 a 0.
[1+1350-1+135025+1350-135+135100010000]
Etapa 2.6.2
Simplifique R1.
[1-125000010000]
[1-125000010000]
[1-125000010000]
Etapa 3
Use the result matrix to declare the final solution to the system of equations.
x-y+25z=0
0=1
0=0
Etapa 4
The solution is the set of ordered pairs that make the system true.
(y-2z5,y,z)
 [x2  12  π  xdx ]