Finite Mathematik Beispiele

$θ = [\begin{array}{c} 0.2 & 0.8 \\ 0.9 & 0.1 \end{array}]$

Schritt 1

Consider the corresponding sign chart.

$[\begin{array}{c} + & - \\ - & + \end{array}]$

Schritt 2

Use the sign chart and the given matrix to find the cofactor of each element.

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Schritt 2.1

Calculate the minor for element $θ_{11}$ .

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Schritt 2.1.1

The minor for $θ_{11}$ is the determinant with row $1$ and column $1$ deleted.

$| \begin{array}{c} 0.1 \end{array} |$

Schritt 2.1.2

Die Determinante einer $1 \times 1$ -Matrix ist das Element selbst.

$θ_{11} = 0.1$

Schritt 2.2

Calculate the minor for element $θ_{12}$ .

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Schritt 2.2.1

The minor for $θ_{12}$ is the determinant with row $1$ and column $2$ deleted.

$| \begin{array}{c} 0.9 \end{array} |$

Schritt 2.2.2

Die Determinante einer $1 \times 1$ -Matrix ist das Element selbst.

$θ_{12} = 0.9$

Schritt 2.3

Calculate the minor for element $θ_{21}$ .

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Schritt 2.3.1

The minor for $θ_{21}$ is the determinant with row $2$ and column $1$ deleted.

$| \begin{array}{c} 0.8 \end{array} |$

Schritt 2.3.2

Die Determinante einer $1 \times 1$ -Matrix ist das Element selbst.

$θ_{21} = 0.8$

Schritt 2.4

Calculate the minor for element $θ_{22}$ .

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Schritt 2.4.1

The minor for $θ_{22}$ is the determinant with row $2$ and column $2$ deleted.

$| \begin{array}{c} 0.2 \end{array} |$

Schritt 2.4.2

Die Determinante einer $1 \times 1$ -Matrix ist das Element selbst.

$θ_{22} = 0.2$

Schritt 2.5

The cofactor matrix is a matrix of the minors with the sign changed for the elements in the $-$ positions on the sign chart.

$[\begin{array}{c} 0.1 & - 0.9 \\ - 0.8 & 0.2 \end{array}]$

Schritt 3

Transpose the matrix by switching its rows to columns.

$[\begin{array}{c} 0.1 & - 0.8 \\ - 0.9 & 0.2 \end{array}]$