1 2 -1 3 4 -2 6 -4 1的逆矩阵
问题描述：
1 2 -1 3 4 -2 6 -4 1的逆矩阵
答
[ A E ] 通过行初等变换,将A化为单位矩阵,同时对E做相同对的行初等变换,其结果即为A的
逆矩阵：
[ 1 2 -1 1 0 0 ] [ 1 2 -1 1 0 0 ] [ 1 0 0 -2 1 0 ] [ 1 0 0 -2 1 0 ]
[ 3 4 -2 0 1 0 ] [ 0 -2 1 -3 1 0 ] [ 0 1 -0.5 1.5 - 0.5 0 ] [ 0 1 -0.5 1.5 -0.5 0 ]
[ 6 -4 1 0 0 1 ] [ 0 -16 7 -6 0 1 ] [ 0 -16 7 -6 0 1 ] [ 0 0 1 -18 8 -1 ]
[ 1 0 0 -2 1 0 ]
[ 0 1 0 -7.5 3.5 -0.5 ]
[ 0 0 1 -18 8 -1 ]
因此 A 的逆矩阵：A^(-1) = [ -2 1 0 ]
[ -7.5 3.5 -0.5 ]
[ -18 8 -1 ]