bernicehb
幼苗
共回答了23个问题采纳率:91.3% 举报
1.由 AX=X+B 得 (A-E)X=B.
(A-E,B) =
1 2 0 2 2
2 0 3 2 1
0 1 -1 0 1
r2-2r1
1 2 0 2 2
0 -4 3 -2 -3
0 1 -1 0 1
r1-2r3,r2+4r3
1 0 2 2 0
0 0 -1 -2 1
0 1 -1 0 1
r2*(-1),r1-2r2,r3+r2
1 0 0 -2 2
0 0 1 2 -1
0 1 0 2 0
r2r3
1 0 0 -2 2
0 1 0 2 0
0 0 1 2 -1
所以 X = (A-E)^-1B =
-2 2
2 0
2 -1
2.增广矩阵 =
k k-1 1 1
k k 1 2
2k 2(k-1) k 2
r2-r1,r3-2r1
k k-1 1 1
0 1 0 1
0 0 k-2 0
当 k≠0 且 k≠2 时,r(A)=3=r(A,b),此时方程组有唯一解.
当 k = 0 时,
增广矩阵-->
0 -1 1 1
0 1 0 1
0 0 -2 0
r1+r2+(1/2)r3
0 0 0 2
0 1 0 1
0 0 -2 0
r(A)=2,r(A,b)=3,故此时方程组无解.
当 k = 2 时,
增广矩阵-->
2 1 1 1
0 1 0 1
0 0 0 0
r1-r2
2 0 1 0
0 1 0 1
0 0 0 0
r(A)=r(A,b)=2
1年前
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