Finite Mathematik Beispiele

Solve Using a Matrix by Row Operations 3x-4y=16 , 6x+8y=-2
3x-4y=16 , 6x+8y=-2
Schritt 1
Write the system as a matrix.
[3-41668-2]
Schritt 2
Ermittele die normierte Zeilenstufenform.
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Schritt 2.1
Multiply each element of R1 by 13 to make the entry at 1,1 a 1.
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Schritt 2.1.1
Multiply each element of R1 by 13 to make the entry at 1,1 a 1.
[33-4316368-2]
Schritt 2.1.2
Vereinfache R1.
[1-4316368-2]
[1-4316368-2]
Schritt 2.2
Perform the row operation R2=R2-6R1 to make the entry at 2,1 a 0.
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Schritt 2.2.1
Perform the row operation R2=R2-6R1 to make the entry at 2,1 a 0.
[1-431636-618-6(-43)-2-6(163)]
Schritt 2.2.2
Vereinfache R2.
[1-43163016-34]
[1-43163016-34]
Schritt 2.3
Multiply each element of R2 by 116 to make the entry at 2,2 a 1.
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Schritt 2.3.1
Multiply each element of R2 by 116 to make the entry at 2,2 a 1.
[1-431630161616-3416]
Schritt 2.3.2
Vereinfache R2.
[1-4316301-178]
[1-4316301-178]
Schritt 2.4
Perform the row operation R1=R1+43R2 to make the entry at 1,2 a 0.
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Schritt 2.4.1
Perform the row operation R1=R1+43R2 to make the entry at 1,2 a 0.
[1+430-43+431163+43(-178)01-178]
Schritt 2.4.2
Vereinfache R1.
[105201-178]
[105201-178]
[105201-178]
Schritt 3
Use the result matrix to declare the final solution to the system of equations.
x=52
y=-178
Schritt 4
The solution is the set of ordered pairs that make the system true.
(52,-178)
3x-4y=16,6x+8y=-2
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