예제

Consider the corresponding sign chart.

The cofactor is the minor with the sign changed if the indices match a ${\displaystyle -}$ position on the sign chart.

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

Multiply element ${\displaystyle a_{11}}$ by its cofactor.

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

Multiply element ${\displaystyle a_{12}}$ by its cofactor.

The minor for ${\displaystyle a_{13}}$ is the determinant with row ${\displaystyle 1}$ and column ${\displaystyle 3}$ deleted.

Multiply element ${\displaystyle a_{13}}$ by its cofactor.

The minor for ${\displaystyle a_{14}}$ is the determinant with row ${\displaystyle 1}$ and column ${\displaystyle 4}$ deleted.

Multiply element ${\displaystyle a_{14}}$ by its cofactor.

Add the terms together.

Choose the row or column with the most ${\displaystyle 0}$ elements. If there are no ${\displaystyle 0}$ elements choose any row or column. Multiply every element in column ${\displaystyle 2}$ by its cofactor and add.

${\displaystyle 0}$에 ${\displaystyle \left|\begin{array}{cc}2& 3\\ 5& 1\end{array}\right|}$을 곱합니다.

${\displaystyle \left|\begin{array}{cc}5& 1\\ 5& 2\end{array}\right|}$의 값을 구합니다.

${\displaystyle \left|\begin{array}{cc}2& 3\\ 5& 2\end{array}\right|}$의 값을 구합니다.

행렬식을 간단히 합니다.

Choose the row or column with the most ${\displaystyle 0}$ elements. If there are no ${\displaystyle 0}$ elements choose any row or column. Multiply every element in row ${\displaystyle 1}$ by its cofactor and add.

${\displaystyle 0}$에 ${\displaystyle \left|\begin{array}{cc}4& 1\\ 0& 2\end{array}\right|}$을 곱합니다.

${\displaystyle \left|\begin{array}{cc}2& 1\\ 1& 2\end{array}\right|}$의 값을 구합니다.

${\displaystyle \left|\begin{array}{cc}2& 4\\ 1& 0\end{array}\right|}$의 값을 구합니다.

행렬식을 간단히 합니다.

Choose the row or column with the most ${\displaystyle 0}$ elements. If there are no ${\displaystyle 0}$ elements choose any row or column. Multiply every element in row ${\displaystyle 1}$ by its cofactor and add.

${\displaystyle 0}$에 ${\displaystyle \left|\begin{array}{cc}5& 1\\ 5& 2\end{array}\right|}$을 곱합니다.

${\displaystyle \left|\begin{array}{cc}2& 1\\ 1& 2\end{array}\right|}$의 값을 구합니다.

${\displaystyle \left|\begin{array}{cc}2& 5\\ 1& 5\end{array}\right|}$의 값을 구합니다.

행렬식을 간단히 합니다.

각 항을 간단히 합니다.

${\displaystyle -49}$를 ${\displaystyle 60}$에 더합니다.

${\displaystyle 11}$를 ${\displaystyle 45}$에 더합니다.

${\displaystyle 56}$를 ${\displaystyle 0}$에 더합니다.