设A=|4 2 3 ,1 1 0,-1 2 3 |,且矩阵X满足AX=A+2X,求X

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设A=|4 2 3 ,1 1 0,-1 2 3 |,且矩阵X满足AX=A+2X,求X
设A=|4 2 3 ,1 1 0,-1 2 3 |,且矩阵X满足AX=A+2X,求X

设A=|4 2 3 ,1 1 0,-1 2 3 |,且矩阵X满足AX=A+2X,求X
由 AX=A+2X 得 (A-2E)X = A.
(A-2E,A) =
2 2 3 4 2 3
1 -1 0 1 1 0
-1 2 1 -1 2 3
r1-2r2,r3+r2
0 4 3 2 0 3
1 -1 0 1 1 0
0 1 1 0 3 3
r1-4r3,r2+r3
0 0 -1 2 -12 -9
1 0 1 1 4 3
0 1 1 0 3 3
r2+r1,r3+r1,r1*(-1)
0 0 1 -2 12 9
1 0 0 3 -8 -6
0 1 0 2 -9 -6
交换行
1 0 0 3 -8 -6
0 1 0 2 -9 -6
0 0 1 -2 12 9
X =
3 -8 -6
2 -9 -6
-2 12 9

设a>1,0 设a>1,0 设a>b>0,证明a^2+1/ab+1/a(a-b)>=4 设a>0且a不等于1,若函数y=a 2x-4a x+3在-1 设A为n阶矩阵,且A^3=0,求(A+2E)^(-1) 设A是3阶矩阵若已知|A|=4则|(2A)^-1|= (1/2)设a>0,|x| 设集合A={x|-1/2 设集合A={x|-1/2 设A={X|-1 设A={x|-1 设集合A={-1 设A={x|1 设A={x|1 设A={x/1 设A={X -1 设A={X|1 设a>0,b>0,且1/a+2/b=4,则2a+3b的最小值RTRTRTRT