Question

求非.X1+X2－X3+X4=1 ,X1－X2+X3－3X4＝1,X1－X2－2X3＋3X4=-1/2

Answer 1

增广矩阵 =

1 1 -1 1 1

1 -1 1 -3 1

1 -1 -2 3 -1/2

r3-r2,r2-r1

1 1 -1 1 1

0 -2 2 -4 0

0 0 -3 6 -3/2

r2*(-1/2),r3*(-1/3)

1 1 -1 1 1

0 1 -1 2 0

0 0 1 -2 1/2

r1-r2,r2+r3

1 0 0 -1 1

0 1 0 0 1/2

0 0 1 -2 1/2

所以方程组的通解为 (1,1/2,1/2,0)^T + c(1,0,2,1)^T.