如何利用MatlAB软件用矩阵求逆、矩阵除法、矩阵分解求下面线性方程组的解?

matlab\u4e2d\u4e0d\u540c\u884c\u5217\u6570\u77e9\u9635\u9664\u6cd5\u95ee\u9898

\u7a0b\u5e8f\uff1a
A = [72 36 12];
B = [1 2 3 1; 3 4 1 1; 4 2 1 1];
[X, Y] = meshgrid(B(1, :), A); % B(1, :)\u4e3b\u8981\u662f\u4e3a\u4e86\u83b7\u53d6B\u7684\u5217\u6570
C = Y ./ B
\u7ed3\u679c\uff1a
C =
72 36 24 72
12 9 36 36
3 6 12 12
\u8bf4\u660e\uff1a\u524d\u63d0\u662f\u8981\u4fdd\u8bc1\u77e9\u9635A\u7684\u5143\u7d20\u4e2a\u6570\u548c\u77e9\u9635B\u7684\u884c\u6570\u76f8\u7b49\uff0c\u800c\u77e9\u9635B\u7684\u5217\u6570\u7a0b\u5e8f\u5df2\u7ecf\u8003\u8651\u5230\u4e86\uff0c\u53ef\u4ee5\u662f\u4efb\u610f\u5217\u6570\u3002

\u5728\u77e9\u9635\u4e2d\u786e\u5b9e\u6ca1\u6709\u542c\u8bf4\u8fc7\u9664\u6cd5\uff0c\u4f46\u662f\u4f60\u5b66\u8fc7\u7ebf\u6027\u4ee3\u6570\u5c31\u8be5\u77e5\u9053
\u77e9\u9635\u7684\u9664\u6cd5\u5176\u5b9e\u5c31\u662f\u201c\u9006\u77e9\u9635\u201d\u7684\u8fd0\u7b97\uff01\u5177\u4f53\u600e\u4e48\u7b97\u53bb\u770b\u4e66\u5427\uff01

A=[5,1,-1,1;1,3,-1,-1;-1,-3,-1,5;1,1,-1,4]
C=inv(A) /*这是求矩阵 A的逆矩阵
B=[1 2 3 4]'
C*B得解
D=[A B]
rref(D) /*这是求矩阵D的行简化阶梯矩阵,得出未知数的解
矩阵的除法:A\B命令

A=[
5,1,-1,1;
1,3,-1,-1;
-1,-3,-1,5;
1,1,-1,4];

b=[1;2;3;4];

xinv=inv(A)*b %求逆
xdiv=A\b %除法
[l,u]=lu(A); %LU分解
y=inv(l)*b;
x=inv(u)*y

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