Matemática discreta Exemplos

Resolva Usando uma Matriz Aumentada -3x-5y=-11 , 4x-2y=32
-3x-5y=-11 , 4x-2y=32
Etapa 1
Write the system as a matrix.
[-3-5-114-232]
Etapa 2
Encontre a forma escalonada reduzida por linhas.
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Etapa 2.1
Multiply each element of R1 by -13 to make the entry at 1,1 a 1.
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Etapa 2.1.1
Multiply each element of R1 by -13 to make the entry at 1,1 a 1.
[-13-3-13-5-13-114-232]
Etapa 2.1.2
Simplifique R1.
[1531134-232]
[1531134-232]
Etapa 2.2
Perform the row operation R2=R2-4R1 to make the entry at 2,1 a 0.
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Etapa 2.2.1
Perform the row operation R2=R2-4R1 to make the entry at 2,1 a 0.
[1531134-41-2-4(53)32-4(113)]
Etapa 2.2.2
Simplifique R2.
[1531130-263523]
[1531130-263523]
Etapa 2.3
Multiply each element of R2 by -326 to make the entry at 2,2 a 1.
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Etapa 2.3.1
Multiply each element of R2 by -326 to make the entry at 2,2 a 1.
[153113-3260-326(-263)-326523]
Etapa 2.3.2
Simplifique R2.
[15311301-2]
[15311301-2]
Etapa 2.4
Perform the row operation R1=R1-53R2 to make the entry at 1,2 a 0.
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Etapa 2.4.1
Perform the row operation R1=R1-53R2 to make the entry at 1,2 a 0.
[1-53053-531113-53-201-2]
Etapa 2.4.2
Simplifique R1.
[10701-2]
[10701-2]
[10701-2]
Etapa 3
Use the result matrix to declare the final solution to the system of equations.
x=7
y=-2
Etapa 4
The solution is the set of ordered pairs that make the system true.
(7,-2)
-3x-5y=-11,4x-2y=32
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 [x2  12  π  xdx ]