考点梳理
1. 乘法规则
(1)行矩阵[a11 a12]与列矩阵\o(\s\up7(b11b21的乘法规则:
[a11 a12]\o(\s\up7(b11b21=[a11×b11+a12×b21].
(2)二阶矩阵\o(\s\up7(a11a21与列向量\o(\s\up7(x0y0的乘法规则:
\o(\s\up7(a11a21 \o(\s\up7(x0y0=\o(\s\up7(a11×x0+a12×y0a21×x0+a22×y0.
(3)两个二阶矩阵相乘的结果仍然是一个矩阵,其乘法法则如下:
\o(\s\up7(a11a21 \o(\s\up7(b11b21=\o(\s\up7(a11×b11+a12×b21a21×b11+a22×b21
(4)两个二阶矩阵的乘法满足结合律,但不满足交换律和消去律.即(AB)C=A(BC),AB≠BA,由AB=AC不一定能推出B=C.