有限数学 示例

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is ${\displaystyle 3\times 2}$ and the second matrix is ${\displaystyle 2\times 3}$.

将第一个矩阵中的每一行乘以第二个矩阵中的每一列。

通过展开所有表达式化简矩阵的每一个元素。

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 ${\displaystyle a_{31}}$ is the determinant with row ${\displaystyle 3}$ and column ${\displaystyle 1}$ deleted.

Multiply element ${\displaystyle a_{31}}$ by its cofactor.

The minor for ${\displaystyle a_{32}}$ is the determinant with row ${\displaystyle 3}$ and column ${\displaystyle 2}$ deleted.

Multiply element ${\displaystyle a_{32}}$ by its cofactor.

The minor for ${\displaystyle a_{33}}$ is the determinant with row ${\displaystyle 3}$ and column ${\displaystyle 3}$ deleted.

Multiply element ${\displaystyle a_{33}}$ by its cofactor.

Add the terms together.

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

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