Álgebra linear Exemplos

Encontre a Pré-Imagem x([[a],[b],[d]])=[[5a+3b-2d],[0a+4b-d]] , [[14],[2]]
,
Etapa 1
Write as an augmented matrix for .
Etapa 2
Write as a linear system of equations.
Etapa 3
Resolva o sistema de equações.
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Etapa 3.1
Move variables to the left and constant terms to the right.
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Etapa 3.1.1
Reordene os fatores em .
Etapa 3.1.2
Mova .
Etapa 3.2
Write the system as a matrix.
Etapa 3.3
Encontre a forma escalonada reduzida por linhas.
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Etapa 3.3.1
Multiply each element of by to make the entry at a .
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Etapa 3.3.1.1
Multiply each element of by to make the entry at a .
Etapa 3.3.1.2
Simplifique .
Etapa 3.3.2
Perform the row operation to make the entry at a .
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Etapa 3.3.2.1
Perform the row operation to make the entry at a .
Etapa 3.3.2.2
Simplifique .
Etapa 3.3.3
Multiply each element of by to make the entry at a .
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Etapa 3.3.3.1
Multiply each element of by to make the entry at a .
Etapa 3.3.3.2
Simplifique .
Etapa 3.3.4
Perform the row operation to make the entry at a .
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Etapa 3.3.4.1
Perform the row operation to make the entry at a .
Etapa 3.3.4.2
Simplifique .
Etapa 3.4
Use the result matrix to declare the final solution to the system of equations.
Etapa 3.5
Write a solution vector by solving in terms of the free variables in each row.
Etapa 3.6
Write the solution as a linear combination of vectors.
Etapa 3.7
Write as a solution set.