求用矩阵解三元方程x+y-z=3-z+y+2x=42y+z+2x-12=0suppose inverse of the L.H.S_数学解答

求用矩阵解三元方程
x+y-z=3
-z+y+2x=4
2y+z+2x-12=0
suppose inverse of the L.H.S coefficient matrix,A^(-1),is -1 1 0
1.333 -1 0.333
-0.667 0 0.333
using inverse matrix method,find the solutions for the above simultaneous equations.

人气：313 ℃　时间：2020-05-19 18:41:03

解答

这个题很简单啊,上面的三元方程组看成Ax=b
A是系数矩阵,b=(3,4,12)T
Ax=b两边左乘A^(-1)
x=A^(-1)b
=|-1 1 0|
|4/3 -1 1/3| * (3,4 ,12)T
|-2/3 0 1/3|
=(1,4,2)T
所以x=1,y=4.z=2