Question

用矩阵的方法截下列代性方程组 X1+X2-X3=1 3X1-2X2+X3=0 X1-X2-X3=2

Answer 1

解: 增广矩阵 =

1 1 -1 1

3 -2 1 0

1 -1 -1 2

r2-3r1,r3-r1

1 1 -1 1

0 -5 4 -3

0 -2 0 1

r3*(-1/2)

1 1 -1 1

0 -5 4 -3

0 1 0 -1/2

r1-r3,r2+5r3

1 0 -1 3/2

0 0 4 -11/2

0 1 0 -1/2

r2*(1/4), r1+r2

1 0 0 1/8

0 0 1 -11/8

0 1 0 -1/2

r2r3

1 0 0 1/8

0 1 0 -1/2

0 0 1 -11/8

方程组的解为: x1=1/8, x2=-1/2,x3=-11/8.

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