三元一次方程组
4个回答
三元一次方程组：
2x-y+8z=3 .(1)
3x+4y-8z=8 .(2)
x+y-2z=-3 .(3)
消去z：(1)+(2):5x+3y=11 .(4)
(1)+(3)*4:6x+3y=-9 .(5)
消去y：(1)+(3):3x+6z=0 .(4)
(2)+(1)*4:11x+24z=20 .(5)
消去x：(3)*2-(1):3y-12z=-9 .(4)
(2)-(3)*3:y-2z=17 .(5)
一般地,三元一次方程组：
a1x+b1y+c1z=d1 .(1)
a2x+b2y+c2z=d2 .(2)
a3x+b3y+c3z=d3 .(3)
消去z：(1)*c2-(2)*c1:(a1c2-a2c1)x+(b1c2-b2c1)y=d1c2-d2c1
(2)*c3-(3)*c2:(a2c3-a3c2)x+(b2c3-b3c2)y=d2c3-d3c2
消去y：(1)*b2-(2)*b1:(a1b2-a2b1)x+(c1b2-c2b1)y=d1b2-d2b1
(2)*b3-(3)*b2:(a2b3-a3b2)x+(c2b3-c3b2)y=d2b3-d3b2
消去x：(1)*a2-(2)*a1:(b1a2-b2a1)x+(c1a2-c2a1)y=d1a2-d2a1
(2)*a3-(3)*a2:(b2a3-b3a2)x+(c2a3-c3a2)y=d2a3-d3a2
