Question

线性代数,应用题,设A=|1 1 -1|,B=|1 -1 0|求矩阵方程XA＝B的解|0 2 2| |1 1 0||1

Answer 1

(A; B) = (A,B上下放置)

1 1 -1

0 2 2

1 -1 0

1 -1 0

1 1 0

2 1 1

c2-c1,c3+c1

1 0 0

0 2 2

1 -2 1

1 -2 1

1 0 1

2 -1 3

c3-c2

1 0 0

0 2 0

1 -2 3

1 -2 3

1 0 1

2 -1 4

c2*(1/2),c3*(1/3)

1 0 0

0 1 0

1 -1 1

1 -1 1

1 0 1/3

2 -1/2 4/3

c1-c3,c2+c3

1 0 0

0 1 0

0 0 1

0 0 1

2/3 1/3 1/3

2/3 5/6 4/3

所以X =

0 0 1

2/3 1/3 1/3

2/3 5/6 4/3

注意:只实施列变换,把上半部分化成单位矩阵