线性方程组 线性方程组1x1+x2 -2x4=-64x1-x2-x3-x4=13x1-x2-x3 =3方程组2X1+MX2-X3-X4=-5NX2-X3-2X4=-11X3-2X4=-T+1参数M N T为何值时,方程组1,2同解
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两个方程组同解的充分必要条件是行向量组等价
设方程组1,2的增广矩阵分别为A1,A2
考虑分块矩阵 H = (A1; A2) --上下放置
则 r(A1)=r(H)=r(A2)
H =1 1 0 -2 -6
4 -1 -1 -1 1
3 -1 -1 0 3
1 m -1 -1 -5
0 n -1 -2 -11
0 0 1 -2 -t+1
r2-4r1,r3-3r1,r4-r1
1 1 0 -2 -6
0 -5 -1 7 25
0 -4 -1 6 21
0 m-1 -1 1 1
0 n -1 -2 -11
0 0 1 -2 -t+1
r2-r31 1 0 -2 -6
0 -1 0 1 4
0 -4 -1 6 21
0 m-1 -1 1 1
0 n -1 -2 -11
0 0 1 -2 -t+1
r3-4r2,r4+(m-1)2,r5+nr2
1 1 0 -2 -6
0 -1 0 1 4
0 0 -1 2 5
0 0 -1 m 4m-3
0 0 -1 n-2 4n-11
0 0 1 -2 -t+1
r4-r3,r5-r3,r6+r3
1 1 0 -2 -6
0 -1 0 1 4
0 0 -1 2 5
0 0 0 m-2 4m-8
0 0 0 n-4 4n-16
0 0 0 0 -t+6由 r(A1)=r(H) 知 m=2,n=4,t=6.易知,此时 r(A2) = 3 = r(A1) = r(H).请问这是哪本教材中的题目,望告知!