求方程组X1-3X2-2X3-X4=1 3X1-8X2-4X3-X4=0 -2X1+X2-4X3+2X4=1 -X1-2X2-6X3+X4=2的解

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求方程组X1-3X2-2X3-X4=13X1-8X2-4X3-X4=0-2X1+X2-4X3+2X4=1-X1-2X2-6X3+X4=2的解求方程组X1-3X2-2X3-X4=13X1-8X2-4X3

求方程组X1-3X2-2X3-X4=1 3X1-8X2-4X3-X4=0 -2X1+X2-4X3+2X4=1 -X1-2X2-6X3+X4=2的解
求方程组X1-3X2-2X3-X4=1 3X1-8X2-4X3-X4=0 -2X1+X2-4X3+2X4=1 -X1-2X2-6X3+X4=2的解

求方程组X1-3X2-2X3-X4=1 3X1-8X2-4X3-X4=0 -2X1+X2-4X3+2X4=1 -X1-2X2-6X3+X4=2的解
增广矩阵 =
1 -3 -2 -1 1
3 -8 -4 -1 0
-2 1 -4 2 1
-1 -2 -6 1 2
r2-3r1,r3+2r1,r4+r1
1 -3 -2 -1 1
0 1 2 2 -3
0 -5 -8 0 3
0 -5 -8 0 3
r4-r3,r3+5r2,r1+3r2
1 0 4 5 -8
0 1 2 2 -3
0 0 2 10 -12
0 0 0 0 0
r1-2r3,r2-r3,r3*(1/2)
1 0 0 -15 16
0 1 0 -8 9
0 0 1 5 -6
0 0 0 0 0
方程组的解为:(16,9,-6,0)'+c(15,8,-5,1)'.

由一式可得:X1=1+3X2+2X3+X4
一式带入二式得:3+17X2+2X3+2X4=0
一式带入三式:-2-5X2=1 由此得出 X2=-3/5
一式带入四式:-1-3X2=4X3=2 由此得出 X3=6/5
从而可以得出X4=24/5 X1=32/5
综上所述:此方程最后结果为
X1=32/5
X2=-3/5
X3=6/5
X4=24/5

X1-3X2-2X3-X4=1 (1)
3X1-8X2-4X3-X4=0 (2)
-2X1+X2-4X3+2X4=1 (3)
-X1-2X2-6X3+X4=2(4)
先消去x4,
(1)+(4),-5x2-8x3=3,(5)
(2)+(4),2x1-10x2-10x3=2,
x1-5x2-5x3=1,(6)
(3)-(4)*2,5x2...

全部展开

X1-3X2-2X3-X4=1 (1)
3X1-8X2-4X3-X4=0 (2)
-2X1+X2-4X3+2X4=1 (3)
-X1-2X2-6X3+X4=2(4)
先消去x4,
(1)+(4),-5x2-8x3=3,(5)
(2)+(4),2x1-10x2-10x3=2,
x1-5x2-5x3=1,(6)
(3)-(4)*2,5x2+8x3=-3,(7)
(5)和(7)同解,设x3=t(任意数),则x2=(-8t-3)/5,
代入(6),x1=-3t-2,
代入(4),x4=x1+2x2+6x3+2=-3t-2+(-16t-6)/5+6t+2=(-t-6)/5.

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