1 / 5

向量组的线性相关性分析

向量组的线性相关性分析. 向量组的线性相关性判别 向量组的最大无关组.  . 向量组的线性相关性判别. 例 1. 讨论向量组 a 1 =(1 3 3 2), a 2 =(2 6 9 5), a 3 =(-1 -3 3 0). 的线性相关性. 解 将向量组中向量按列向量排列成矩阵并用命令 rref 化简 , 输入如下 MATLAB 命令 :. >> A=[1 3 3 2;2 6 9 5;-1 -3 3 0]; >> A=A′; >> format rat >> rref(A). 运行结果为. ans = 1 0 -5

washi
Download Presentation

向量组的线性相关性分析

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 向量组的线性相关性分析 向量组的线性相关性判别 向量组的最大无关组  

  2. 向量组的线性相关性判别 例1.讨论向量组a1=(1 3 3 2), a2=(2 6 9 5), a3=(-1 -3 3 0) 的线性相关性. 解 将向量组中向量按列向量排列成矩阵并用命令rref化简,输入如下MATLAB命令: >> A=[1 3 3 2;2 6 9 5;-1 -3 3 0]; >> A=A′; >> format rat >> rref(A) 运行结果为 ans = 1 0 -5 0 1 2 0 0 0 0 0 0 因其对应的阶梯形阵的秩为2小于3,故向量组a1, a2, a3线性相关.

  3. 例2.判断向量组a1=(1 2 0 1), a2=(1 3 0 -1), a3=(-1 -1 1 0) 是否线性相关,并求秩. 解 将向量组中向量按列向量排列成矩阵并用命令rref化简,输入如下MATLAB命令: >> A=[1 2 0 1;1 3 0 -1;-1 -1 1 0]; >> A=A′; >> format rat >> rref(A) 运行结果为 ans = 1 0 0 0 1 0 0 0 1 0 0 0 可见最简矩阵的秩为3,故向量组a1,a2,a3线性无关.

  4. 向量组的最大无关组 例3.求下列向量组的秩和一个最大线性无关组,并将其余向量用该最大无关组线性表示. a1=(2 -1 3 5), a2=(4 -3 1 3), a3=(3 -2 3 4), a4=(4 -1 15 17), a5=(7 -6 -7 0) 解 将向量组中向量按列向量排列成矩阵并用命令rref化简,输入如下MATLAB命令: >> A=[2 -1 3 5;4 -3 1 3;3 -2 3 4;4 -1 15 17;7 -6 -7 0]; >> A=A′; >> format rat >> rref(A) 运行结果为

  5. ans = 1 0 0 2 1 0 1 0 -3 5 0 0 1 4 -5 0 0 0 0 0 矩阵ans中有3个不全为零的行向量,所以矩阵A的秩为3.最简矩阵第一列、第二列和第三列向量线性无关,所以对应于原矩阵A的前三个行向量线性无关,即原向量组中一个最大无关组为a1, a2和a3. 矩阵ans中第四、五列中分别有三个非零元素,可将a4和a5线性表示为 a4=2a1-3a2+4a3 , a5=a1+5a2-5a3

More Related