Question

线性代数球全部解X1- X2 +2X3 +2X4=入2X1+X2 +4X3+ X4=5X1+2X2+2X3 - X4 =

Answer 1

增广矩阵 =

1 -1 2 2 λ

2 1 4 1 5

1 2 2 -1 4

r1-r3,r2-2r3

0 -3 0 3 λ-4

0 -3 0 3 -3

1 2 2 -1 4

r1-r2,r2*(-1/3),r3-2r2

0 0 0 0 λ-1

0 1 0 -1 1

1 0 2 1 2

所以,λ-1=0 即λ=1时方程组有解,此时增广矩阵化为

1 0 2 1 2

0 1 0 -1 1

0 0 0 0 0

方程组的解为:(2,1,0)'+c1(2,0,-1,0)'+c2(1,-1,0,-1)'.

唉,累了...