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Algèbre linéaire Exemples
Étape 1
To determine if the columns in the matrix are linearly dependent, determine if the equation has any non-trivial solutions.
Étape 2
Write as an augmented matrix for .
Étape 3
Étape 3.1
Multiply each element of by to make the entry at a .
Étape 3.1.1
Multiply each element of by to make the entry at a .
Étape 3.1.2
Simplifiez .
Étape 3.2
Perform the row operation to make the entry at a .
Étape 3.2.1
Perform the row operation to make the entry at a .
Étape 3.2.2
Simplifiez .
Étape 3.3
Perform the row operation to make the entry at a .
Étape 3.3.1
Perform the row operation to make the entry at a .
Étape 3.3.2
Simplifiez .
Étape 3.4
Multiply each element of by to make the entry at a .
Étape 3.4.1
Multiply each element of by to make the entry at a .
Étape 3.4.2
Simplifiez .
Étape 3.5
Perform the row operation to make the entry at a .
Étape 3.5.1
Perform the row operation to make the entry at a .
Étape 3.5.2
Simplifiez .
Étape 3.6
Perform the row operation to make the entry at a .
Étape 3.6.1
Perform the row operation to make the entry at a .
Étape 3.6.2
Simplifiez .
Étape 4
Remove rows that are all zeros.
Étape 5
Write the matrix as a system of linear equations.
Étape 6
Since the only solution to is the trivial solution, the vectors are linearly independent.
Indépendant linéairement