Lineare Algebra Beispiele

Bestimme, ob linear abhängig s={[[-7],[5],[1]],[[-6],[5],[0]]}
Schritt 1
To determine if the columns in the matrix are linearly dependent, determine if the equation has any non-trivial solutions.
Schritt 2
Write as an augmented matrix for .
Schritt 3
Ermittele die normierte Zeilenstufenform.
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Schritt 3.1
Multiply each element of by to make the entry at a .
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Schritt 3.1.1
Multiply each element of by to make the entry at a .
Schritt 3.1.2
Vereinfache .
Schritt 3.2
Perform the row operation to make the entry at a .
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Schritt 3.2.1
Perform the row operation to make the entry at a .
Schritt 3.2.2
Vereinfache .
Schritt 3.3
Perform the row operation to make the entry at a .
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Schritt 3.3.1
Perform the row operation to make the entry at a .
Schritt 3.3.2
Vereinfache .
Schritt 3.4
Multiply each element of by to make the entry at a .
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Schritt 3.4.1
Multiply each element of by to make the entry at a .
Schritt 3.4.2
Vereinfache .
Schritt 3.5
Perform the row operation to make the entry at a .
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Schritt 3.5.1
Perform the row operation to make the entry at a .
Schritt 3.5.2
Vereinfache .
Schritt 3.6
Perform the row operation to make the entry at a .
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Schritt 3.6.1
Perform the row operation to make the entry at a .
Schritt 3.6.2
Vereinfache .
Schritt 4
Remove rows that are all zeros.
Schritt 5
Write the matrix as a system of linear equations.
Schritt 6
Since the only solution to is the trivial solution, the vectors are linearly independent.
Linear unabhängig