线性代数示例

$[\begin{array}{c} 1 & 2 & 0 \\ 0 & - 1 & 7 \\ 2 & - 3 & - 1 \end{array}] [\begin{array}{c} 2 & 0 & 5 \\ 0 & 2 & 0 \\ 3 & 1 & 5 \end{array}]$

解题步骤 1

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 $3 \times 3$ and the second matrix is $3 \times 3$ .

解题步骤 2

将第一个矩阵中的每一行乘以第二个矩阵中的每一列。

$[\begin{array}{c} 1 \cdot 2 + 2 \cdot 0 + 0 \cdot 3 & 1 \cdot 0 + 2 \cdot 2 + 0 \cdot 1 & 1 \cdot 5 + 2 \cdot 0 + 0 \cdot 5 \\ 0 \cdot 2 - 0 + 7 \cdot 3 & 0 \cdot 0 - 1 \cdot 2 + 7 \cdot 1 & 0 \cdot 5 - 0 + 7 \cdot 5 \\ 2 \cdot 2 - 3 \cdot 0 - 1 \cdot 3 & 2 \cdot 0 - 3 \cdot 2 - 1 \cdot 1 & 2 \cdot 5 - 3 \cdot 0 - 1 \cdot 5 \end{array}]$

解题步骤 3

通过展开所有表达式化简矩阵的每一个元素。

$[\begin{array}{c} 2 & 4 & 5 \\ 21 & 5 & 35 \\ 1 & - 7 & 5 \end{array}]$

线性代数 示例

线性代数示例