Lineare Algebra Beispiele

Ermittle die Umkehrfunktion [[0,0,0,1],[1,0,1,1],[1,1,1,1],[0,0,0,1]]
Schritt 1
Find the determinant.
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Schritt 1.1
Choose the row or column with the most elements. If there are no elements choose any row or column. Multiply every element in row by its cofactor and add.
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Schritt 1.1.1
Consider the corresponding sign chart.
Schritt 1.1.2
The cofactor is the minor with the sign changed if the indices match a position on the sign chart.
Schritt 1.1.3
The minor for is the determinant with row and column deleted.
Schritt 1.1.4
Multiply element by its cofactor.
Schritt 1.1.5
The minor for is the determinant with row and column deleted.
Schritt 1.1.6
Multiply element by its cofactor.
Schritt 1.1.7
The minor for is the determinant with row and column deleted.
Schritt 1.1.8
Multiply element by its cofactor.
Schritt 1.1.9
The minor for is the determinant with row and column deleted.
Schritt 1.1.10
Multiply element by its cofactor.
Schritt 1.1.11
Add the terms together.
Schritt 1.2
Mutltipliziere mit .
Schritt 1.3
Mutltipliziere mit .
Schritt 1.4
Mutltipliziere mit .
Schritt 1.5
Berechne .
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Schritt 1.5.1
Choose the row or column with the most elements. If there are no elements choose any row or column. Multiply every element in row by its cofactor and add.
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Schritt 1.5.1.1
Consider the corresponding sign chart.
Schritt 1.5.1.2
The cofactor is the minor with the sign changed if the indices match a position on the sign chart.
Schritt 1.5.1.3
The minor for is the determinant with row and column deleted.
Schritt 1.5.1.4
Multiply element by its cofactor.
Schritt 1.5.1.5
The minor for is the determinant with row and column deleted.
Schritt 1.5.1.6
Multiply element by its cofactor.
Schritt 1.5.1.7
The minor for is the determinant with row and column deleted.
Schritt 1.5.1.8
Multiply element by its cofactor.
Schritt 1.5.1.9
Add the terms together.
Schritt 1.5.2
Mutltipliziere mit .
Schritt 1.5.3
Mutltipliziere mit .
Schritt 1.5.4
Mutltipliziere mit .
Schritt 1.5.5
Vereinfache die Determinante.
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Schritt 1.5.5.1
Addiere und .
Schritt 1.5.5.2
Addiere und .
Schritt 1.6
Vereinfache die Determinante.
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Schritt 1.6.1
Addiere und .
Schritt 1.6.2
Addiere und .
Schritt 1.6.3
Subtrahiere von .
Schritt 2
There is no inverse because the determinant is .