将矩阵(1 1 -1 2;0 2 -4 6 ;1 3 -4 2 ;2 4 -5 4)求行阶梯形,行最简形
问题描述：
将矩阵(1 1 -1 2;0 2 -4 6 ;1 3 -4 2 ;2 4 -5 4)求行阶梯形,行最简形
答
r3-r1,r4-2r1
1 1 -1 2
0 2 -4 6
0 2 -3 0
0 2 -3 0
r2-r3,r4-r3
1 1 -1 2
0 0 -1 6
0 2 -3 0
0 0 0 0
r2r3
1 1 -1 2
0 2 -3 0
0 0 -1 6
0 0 0 0
(行阶梯形)
r3*(-1),r1+r3,r2+3r3
1 1 0 -4
0 2 0 -18
0 0 1 -6
0 0 0 0
r2*(1/2),r2-r1
1 0 0 5
0 1 0 -9
0 0 1 -6
0 0 0 0
(行最简形)