用消元法解线性方程组x1+x2+2x3+4x4=33x1+x2+6x3+2x4=3-x1+2x2-2x3+x4=1麻烦用
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用消元法解线性方程组
x1+x2+2x3+4x4=3
3x1+x2+6x3+2x4=3
-x1+2x2-2x3+x4=1
麻烦用矩阵做,做到最简形以后,再解出方程.
答案是x1=-2k+1/2,x2=1/2,x3=k,x4=1/2
x1+x2+2x3+4x4=3
3x1+x2+6x3+2x4=3
-x1+2x2-2x3+x4=1
麻烦用矩阵做,做到最简形以后,再解出方程.
答案是x1=-2k+1/2,x2=1/2,x3=k,x4=1/2
增广矩阵 =
1 1 2 4 3
3 1 6 2 3
-1 2 -2 1 1
r2-3r1,r3+r1
1 1 2 4 3
0 -2 0 -10 -6
0 3 0 5 4
r2*(-1/2),r1-r2,r3-3r2
1 0 2 -1 0
0 1 0 5 3
0 0 0 -10 -5
r3*(-1/10),r1+r3,r2-5r3
1 0 2 0 1/2
0 1 0 0 1/2
0 0 0 1 1/2
得同解方程组:
x1 = -2x3 + 1/2
x2 = 1/2
x4 = 1/2
令x3=k,即得
x1=-2k+1/2,x2=1/2,x3=k,x4=1/2
1 1 2 4 3
3 1 6 2 3
-1 2 -2 1 1
r2-3r1,r3+r1
1 1 2 4 3
0 -2 0 -10 -6
0 3 0 5 4
r2*(-1/2),r1-r2,r3-3r2
1 0 2 -1 0
0 1 0 5 3
0 0 0 -10 -5
r3*(-1/10),r1+r3,r2-5r3
1 0 2 0 1/2
0 1 0 0 1/2
0 0 0 1 1/2
得同解方程组:
x1 = -2x3 + 1/2
x2 = 1/2
x4 = 1/2
令x3=k,即得
x1=-2k+1/2,x2=1/2,x3=k,x4=1/2
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