线性代数 示例

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.

将 ${\displaystyle 0}$ 乘以 ${\displaystyle \left|\begin{array}{cc}2& 3\\ 5& 1\end{array}\right|}$。

计算 ${\displaystyle \left|\begin{array}{cc}5& 1\\ 5& 2\end{array}\right|}$。

计算 ${\displaystyle \left|\begin{array}{cc}2& 3\\ 5& 2\end{array}\right|}$。

化简行列式。

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.

将 ${\displaystyle 0}$ 乘以 ${\displaystyle \left|\begin{array}{cc}4& 1\\ 0& 2\end{array}\right|}$。

计算 ${\displaystyle \left|\begin{array}{cc}2& 1\\ 1& 2\end{array}\right|}$。

计算 ${\displaystyle \left|\begin{array}{cc}2& 4\\ 1& 0\end{array}\right|}$。

化简行列式。

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.

将 ${\displaystyle 0}$ 乘以 ${\displaystyle \left|\begin{array}{cc}5& 1\\ 5& 2\end{array}\right|}$。

计算 ${\displaystyle \left|\begin{array}{cc}2& 1\\ 1& 2\end{array}\right|}$。

计算 ${\displaystyle \left|\begin{array}{cc}2& 5\\ 1& 5\end{array}\right|}$。

化简行列式。

化简每一项。

将 ${\displaystyle -49}$ 和 ${\displaystyle 60}$ 相加。

将 ${\displaystyle 11}$ 和 ${\displaystyle 45}$ 相加。

将 ${\displaystyle 56}$ 和 ${\displaystyle 0}$ 相加。