✔ 最佳答案
1.判斷唯一解或無限多解x+3y+0=0.......a4x+3y-z=0......b8x+3y+3z=0.....ca-b: 3x-z=0 => z=3xb-c: 4x+4z=0 => z=-x=\=3x => 矛盾方程式=無解
2.判斷唯一解或無限多解12x+5y+z=012x+4y-z=0add: 24x=9y => x=3y/8Subtract: y+2z=0 => z=-y/2=-4y/8x:y:z=3:8:-4 => 無限多解
3.高思消去法或高斯-喬登消去法來求解x+2y=0.......ax+y=6........b3x-2y=8......ca+c: 4x=8 => x=22b-a: x=12=\=2 => 矛盾方程式=無解
4.唯一解 無解 無限多解x+y=0y+z=0x+z=0add: 2(x+y+z)=0 => x+y+z=0ax+by+cz=0
x+y+z=0|a b c a|
|1 1 1 1|=(a-b,b-c,c-a)x=(b-c)z/(a-b)y=(c-a)z/(a-b)x:y:z=(b-c):(c-a):(a-b)x=(b-c)ky=(c-a)kz=(a-b)k1.k=0 => x=y=z=0 => 唯一解2.a-b=0 => a=b => x+y=1, z=0, x=y=0 => 矛盾方程式=無解3.k=其他實數 => 無限多解