二阶行列式及逆矩阵.ppt

* * Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 二阶行列式与逆矩阵 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 复习提问 如何用几何方法求矩阵的逆矩阵? 它的一般步骤: 如何从代数角度思考逆矩阵的问题呢? 逆矩阵的定义: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 什么矩阵存在逆矩阵? 根据逆矩阵的定义 是否存在逆矩阵,若存在,试着求出其逆矩阵 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 实数a,b,c,d必须满足方程组 解得 所以 有 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 验证 显然已有 MP=I Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 根据逆矩阵的定义 实数u,v,s,t必须满足方程组 显然无解 矩阵N不存在逆矩阵 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 抽象概括 由逆矩阵的定义,有 实数u,v,s,t必须满足 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 即 满足怎样条件有解? 验证 MN=NM=I 当ad-bc≠0时有解 当ad-bc=0时方程组无解,矩阵M不存在逆矩阵 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 行列式 判断一个矩阵是否有逆矩阵就要判断它的行列式是否为零 注 行列式与矩阵之间的差别 行列式是一个数,矩阵是一个数表 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 定理 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例 解 所以矩阵M存在逆矩阵M-1,且 验证 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 练习 求下列矩阵的逆矩阵 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.