Question

用克莱姆法则解方程组 解下这两题

Answer 1

2、D=| 1 2 4
5 1 2
3 -1 1|
=1*1*1+2*2*3+4*5*(-1)-4*1*3-2*5*1-1*(-1)*2
=1+12-20-12-10+2
=-27≠0
Dx=| 31 2 4
29 1 2
10 -1 1|
=31*1*1+2*2*10+4*29*(-1)-4*1*10-2*29*1-31*(-1)*2
=31+40-116-40-58+62
=-81
Dy=| 1 31 4
5 29 2
3 10 1|
=1*29*1+31*2*3+4*5*10-4*29*3-31*5*1-1*10*2
=29+186+200-348-155-20
=-108
Dz=| 1 2 31
5 1 29
3 -1 10|
=1*1*10+2*29*3+31*5*(-1)-31*1*3-2*5*10-1*(-1)*29
=10+174-155-93-100+29
=-135
x=Dx/D
=-81/(-27)
=3
y=Dy/D
=-108/(-27)
=4
z=Dz/D
=-135/(-27)
=5
3、D=0
| λ 1 1
1 μ 1 =0
1 2μ 1|
λμ*1+1*1*1+1*1*2μ-1*μ*1-1*1*1-λ*2μ*1=0
μ-λμ=0
μ(1-λ)=0
μ=0
1-λ=0
λ=1