matlab中用逆矩阵法,solve,rref法求解线性方程组的解.2x+3y+z=5 2x+3y+z=8 matlab求解线性方程组{2x+3y=1 -4x-6y=-...
matlab\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4{2x+3y=1 -4x-6y=-2\u7684\u89e3\uff1f\u89e3 2x-3y=1/2y+1 \u4e24\u8fb9\u4e58\u4ee52\u6574\u7406\u5f97\uff1a 4x-7y=2 \u2460 4x-6y=2-2y \u6574\u7406\u5f97\uff1a x-y=1/2 \u2461 \u5c06\u2461\u53d8\u5f62\u4e3a\uff1a x=y+1/2 \u4ee3\u5165\u2460\u5f97\uff1a 4(y+1/2)-7y=2 4y-7y+2=2 y=0 \u2234x=1/2
\u516c\u5f0f\u5e94\u8be5\u662f[x,y]=solve('2*x+3*y=1','-4*x-6*y=-2','x','y')\uff0c\u4f46\u662f\u8fd9\u4e24\u4e2a\u5f0f\u5b50\u8868\u8fbe\u7684\u662f\u540c\u4e00\u6761\u76f4\u7ebf\uff0c\u89e3\u8fd9\u65b9\u7a0b\u7ec4\u6ca1\u6709\u610f\u4e49
A=[ 2 3 13 2 5
1 3 2];
b1=[5 7 6]';
b2=[8 9 10]';
逆矩阵
rats(inv(A)*b1)
ans =
-1/9
13/9
8/9
rats(inv(A)*b2)
ans =
-5/6
17/6
7/6
solve:
res=solve('2*x+3*y+z=5','3*x+2*y+5*z=7','x+3*y+2*z=6');[res.x res.y res.z]
ans =
[ -1/9, 13/9, 8/9]
res=solve('2*x+3*y+z=8','3*x+2*y+5*z=9','x+3*y+2*z=10');[res.x res.y res.z]
ans =
[ -5/6, 17/6, 7/6]
rref法：
R=rref([A b1])
R =
1 0 0 -1/9
0 1 0 13/9
0 0 1 8/9
R=rref([A b2])
R =
1 0 0 -5/6
0 1 0 17/6
0 0 1 7/6
绛旓細A=[ 2 3 1 3 2 5 1 3 2];b1=[5 7 6]';b2=[8 9 10]';閫嗙煩闃 rats(inv(A)*b1)ans = -1/9 13/9 8/9 rats(inv(A)*b2)ans = -5/6 17/6 7/6 solve:res=solve('2*x+3*y+z=5','3*x+2*y+5*z=7','x+3*y+2*z=6');[res.x res.y res.z]ans = [...
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