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RowReduce

Usage

RowReduce[m] 给出矩阵m的行约简形式.


Notes

• 例如: RowReduce[  3, 1, a ,  2, 1, b  ]LongRightArrow .
RowReduce进行Gaussian消去法,把行的倍数加在一起以尽可能生成0元素.最后矩阵化成梯状形式.
• 如果 m 是一个非退化方阵, RowReduce[m]IdentityMatrix[m].
• 如果m 是一个具有  行和超过  行的充分非退化三角阵 , 则RowReduce[m]的前  列将形成一个单位矩阵.
RowReduce 同时适合于数值矩阵和符号矩阵.
RowReduce[m, Modulus -> n]n 为模进行行化简.
RowReduce[m, ZeroTest -> test] 计算 test[ m[[i, j]] ] 以确定矩阵元素是否为0。
• 参见Mathematica 全书 : 3.7.8节.
• 实现注释: 参见 A.9.4节.
Further Examples

A non-singular matrix can be row-reduced to the identity matrix.

In[1]:=  

Out[1]//MatrixForm=

For non-zero singular matrices, the last row reduces to zero and the last column cannot be zeroed (if not zero from the start).

In[2]:=  

Out[2]//MatrixForm=

You can use RowReduce to solve a system of linear equations. This gives the solution to the linear system {x + y - z Equal 1, x + 2y + 5z Equal 1, 2x + y + 3z Equal -2}.

In[3]:=  

Out[3]=

Column 1 corresponds to the variable x, column 2 to the variable y and column 3 to the variable z. So the solution of the system is x =  , y =  , and z =  .