求方程组:x1+x2-x3+2x4=3,2x1+x2-3x4 =1,-2x1-2x3+10x4=4(2) X1-4x2+2x3-3x4=114x1+3x2+6x3-x4=-12x1+4x2+2x3+x4=-6

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 21:23:35
求方程组:x1+x2-x3+2x4=3,2x1+x2-3x4=1,-2x1-2x3+10x4=4(2)X1-4x2+2x3-3x4=114x1+3x2+6x3-x4=-12x1+4x2+2x3+x4=

求方程组:x1+x2-x3+2x4=3,2x1+x2-3x4 =1,-2x1-2x3+10x4=4(2) X1-4x2+2x3-3x4=114x1+3x2+6x3-x4=-12x1+4x2+2x3+x4=-6
求方程组:x1+x2-x3+2x4=3,2x1+x2-3x4 =1,-2x1-2x3+10x4=4
(2) X1-4x2+2x3-3x4=11
4x1+3x2+6x3-x4=-1
2x1+4x2+2x3+x4=-6

求方程组:x1+x2-x3+2x4=3,2x1+x2-3x4 =1,-2x1-2x3+10x4=4(2) X1-4x2+2x3-3x4=114x1+3x2+6x3-x4=-12x1+4x2+2x3+x4=-6
(1) 增广矩阵 =
1 1 -1 2 3
2 1 0 -3 1
-2 0 -2 10 4
r3+r2,r2-2r1
1 1 -1 2 3
0 -1 2 -7 -5
0 1 -2 7 5
r1+r2,r3+r2,r2*(-1)
1 0 1 -5 -2
0 1 -2 7 5
0 0 0 0 0
方程组的通解为:(-2,5,0,0)^T+c1(-1,2,1,0)^T+c2(5,-7,0,1)^T.
(2)
增广矩阵 =
1 -4 2 -3 11
4 3 6 -1 -1
2 4 2 1 -6
r2-4r1,r3-2r1
1 -4 2 -3 11
0 19 -2 11 -45
0 12 -2 7 -28
r2-r3
1 -4 2 -3 11
0 7 0 4 -17
0 12 -2 7 -28
r2*(1/7),r1+4r2,r3-12r2
1 0 2 -5/7 9/7
0 1 0 4/7 -17/7
0 0 -2 1/7 8/7
r1+r3,r3*(-1/2)
1 0 0 -4/7 17/7
0 1 0 4/7 -17/7
0 0 1 -1/14 -4/7
方程组的通解为:(17/7,-17/7,-4/7,0)^T + c(8,-8,1,14)^T.

(1)
x1 = -x3 + 5x4 - 2
x2 = 2x3 - 7x4 + 5
(x3,x4为自由变量)
(2)
x1 = 17 / 7 + 4x4 / 7
x2 = -17 / 7 - 4x4 / 7
x3 = -4 / 7 + x4 /14谢谢了,能否把解题步骤写详细一点啊,我要的是解题过程学过矩阵没?用矩阵的初等行变换求没有学过啊,...

全部展开

(1)
x1 = -x3 + 5x4 - 2
x2 = 2x3 - 7x4 + 5
(x3,x4为自由变量)
(2)
x1 = 17 / 7 + 4x4 / 7
x2 = -17 / 7 - 4x4 / 7
x3 = -4 / 7 + x4 /14

收起

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 判断方程组是否有解;如方程组有无穷多个解时,求方程组的全部解.方程组 x1-x2-x3+x4=0x1+x2-x3-3x4=1x1-2x2-x3+3x4=1/2 2X1+X2-5X3+X4=8,X1-3X2-6X4=9,2X2-X3+2X4=-5,X1+4X2-7X3+6X4=0.求这个方程组的解 若X1,X2,X3,X4,X5 满足方程组:2X1+X2+X3+X4+X5=6,①X1+2X2+X3+X4+X5=12 ②X1+X2+2X3+X4+X5=24 ③X1+X2+X3+2X4+X5=48 ④X1+X2+X3+X4+2X5=96 ⑤⑴求X1+X2+X3+X4+X5的值;⑵求3X3+2X4-X5有必要说明一下,凡是跟在X后面的数字都是小 若x1,x2,x3,x4,x5满足方程组:x1-x2+x3=1 x2-x3+x4=2 x3-x4+x5=3 x4-x5+x1=4 x5-x1+x2=5 求x2,x3,x4的少打了个字,是求x2,x3,x4的值 求方程组:x1+x2-x3+2x4=3,2x1+x2-3x4 =1,-2x1-2x3+10x4=4(2) X1-4x2+2x3-3x4=114x1+3x2+6x3-x4=-12x1+4x2+2x3+x4=-6 若X1-X5满足下列方程组2乘X1 +X2+X3+X4+X5=6X1+ 2乘X2 +X3+X4+X5=12X1+X2+ 2乘X3 +X4+X5=24X1+X2+X3+ 2乘X4 +X5=48X1+X2+X3+X4+ 2乘X5 =96求3乘X4+X5的值. 解方程组X1-2x2+3x3-x4=1,3x1-x2+5x3-3x4=2,2x1+x2+2x3-2x4=3 解方程组(x1+2x2+2x3+x4=0,2x1+x2-2x3-2x4=0,x1-x2-4x3-3x4=0) 解非线性方程组 x1+2x2+2x3+x4=0 2x1+x2-2x3-2x4=0 x1-x2-4x3-3x4=0 解方程组 x1+2x2+2x3+x4=0 2x1+x2-2x3-2x4=0 x1-x2-4x3-3x4=0 写出方程组2*x1+x2-x3+x4=1,x1+2*x2+x3-x4=2,x1+x2+2*x3+x4=3的通解? 求非齐次线方程组的通解 :2x1+x2-x3+x4=1 x1+2x2+x3-x4=2 x1+x2+2x3+x4=3 具体写出方程组:2x1+x2-x3+x4=1;x1+2x2+x3-x4=2;x1+x2+2x3+x4=3的通解 解一道方程组x1+x2+x3=5,x2+x3+x4=1,x3+x4+x5=-5,x4+x5+x1=-3,x5+x1+x2=2 解方程组X2+X3+X4=1 X1+X2+X3=5 X3+X4+X5=-5 X4+X5+X1=-3 X5+X1+X2=2 求x1x2x3x4x5百度里的已经看过了,求别的方式,不准抄袭 求齐次线性方程组的一个基础解系,并求方程组的通解2x1-3x2+x3+5x4=0 -3x1+x2+2x3-4x4=0-x1-2x2+3x3+x4=0 求方程组x1+3x2+x3+2x4+4x5=3 2x1-x2+8x3+7x4+2x5=9 4x1+5x2+6x3+11x4+10x5=15的全部解线性代数