补充1: 高斯-若尔当消元法(Gauss-Jordan Elimination) 相对于高斯消元法,高斯-若尔当消元法最后的得到线性方程组更容易求解,它得到的是简化行列式。其转化后的增高矩阵形式如下,因此它可以直接求出方程的解,而无需使用替换算法。但是,此算法的效率较低。 例子如下: 解为 个人感觉区别就是对每行进行了归一化处理...
高斯-若尔当消元法(Gauss-Jordan Elimination) 高斯消元法,是线性代数中的一个算法,可用来求解线性方程组,并可以求出矩阵的秩,以及求出可逆方阵的逆矩阵。高斯消元法的原理是:若用初等行变换将增广矩阵 化为 ,则AX = B与CX = D是同解方程组。 所以我们可以用初等行变换把增广矩阵转换为行阶梯阵,然后回代...
This paper deals with the algorithm for computing outer inverse with prescribed range and null space, based on the choice of an appropriate matrix G and Gauss–Jordan elimination of the augmented matrix [G|I]. The advantage of such algorithms is the fact that one can compute various ...
这里先给出一些铺垫:既然求逆,前提肯定是方阵A是可逆的,对矩阵A进行几种初等变换可以得到上三角矩阵U,假设分别经过了3种初等变换E,F,G最后得到U,那么A=GFEU,同时A总可以分解为一个下三角矩阵与一个上三角矩阵相乘,即A=LU,其中L为下三角矩阵,因此L=GFE。 当将A和E放在一起组成一个新的矩阵时,将A变化为...
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#include<cstdio>#include<cmath>#include<algorithm>#defineeps 1e-8usingnamespacestd;doublea[55][55],ans[55];intd;intgauss_jordan(intn){//a为增广矩阵intr,w=0;for(inti=0;i<n&&w<n;w++,i++){//进行到第i列,第w行intr=w;for(intj=w+1;j<n;j++)if(fabs(a[j][i])>fabs(a[r...
Gauss-Jordan Elimination
(a) Solve the following system by transforming the augmented matrix to reduced echelon form (Gauss-Jordan elimination). Indicate the elementary row operations you performed. x1+x2−x5x2+2x3+x4+3x5x1−x3+x4+x5=1=1=0x1+x2−x5=1x2+2x3+x4+3x5=1x1−x3+x4+x5=0 (b) Determine ...
Gauss–Jordan elimination is a procedure for converting a matrix to reduced row echelon form using elementary row operations. It is a refinement of Gaussian elimination. The reduced row echelon form of a matrix is unique, but the steps of the procedure are not. Two linear systems are equivalent...
Gauss-Jordan Elimination Calculator, an online calculator that will show step by step row operations in performing Gauss-Jordan elimination to reduce a matrix to its reduced row echelon form.