Question

用基础解系表示如下线性方程租的全部解 X1+X2-3X3-X4=1 3X1-X2-3X3+4X4=4 X1+5X2-9X

Answer 1

解: 增广矩阵 =

1 1 -3 -1 1

3 -1 -3 4 4

1 5 -9 -8 0

r2-3r1, r3-r1

1 1 -3 -1 1

0 -4 6 7 1

0 4 -6 -7 -1

r3+r2

1 1 -3 -1 1

0 -4 6 7 1

0 0 0 0 0

r2*(-1/4)

1 1 -3 -1 1

0 1 -3/2 -7/4 -1/4

0 0 0 0 0

r1-r2

1 0 -3/2 3/4 5/4

0 1 -3/2 -7/4 -1/4

0 0 0 0 0

通解为: (5/4,-1/4,0,0)^T + c1(3,3,-2,0)^T + c2(3,-7,0,-4)^T, c为任意常数.