若矩阵[1 x 0 1]^3=[1 1 0 1]求x
问题描述：
若矩阵[1 x 0 1]^3=[1 1 0 1]求x
答
设E为单位阵, B = [0, x; 0, 0],
则[1, x; 0, 1] = E+B.
并可知B² = 0.
于是[1, x; 0, 1]³ = (E+B)³ = E+3B+3B²+B³ = E+3B = [1, 3x; 0, 1].
由[1, 3x; 0, 1] = [1, x; 0, 1]³ = [1, 1; 0, 1]即解得x = 1/3.
答
1 x 1 x 1 x
0 1 0 1 0 1=
1 2x 1 x
0 1 0 1=
1 3x
0 1
x=1/3