Question

如何将矩阵分为几个较小的矩阵,以找到不为人知的变量?

例如,考虑到:

“new

如何通过将3x3矩阵分成小矩阵(1x1或其他)来解决这个问题,以找到x、 y、z和u的数值?

Answer 1

在new图像中,你用一些身份对不知名的矩阵表示孤立:

A * X = B
(inv(A)) * A * X = (inv(A)) * B
I * X = (inv(A)) * B
X = (inv(A)) * B

在Matlab:

A = [1, 2; 0, 1]
B = [4, 7; 4, 6]
X = inv(A) * B

产出:

Answer 2

您的矩阵层面是同意的,还是我没有的东西?

Edit: The code from Jeff E will work fine on smaller matrices. For bigger matrices you will need to use backward substitution or some other algorithm, mainly because matrix inversion is a memory intensive task.

Answer 3

为了解决A*X=B的等式,您应使用backslash营运人,因为其中明确使用了逆文。

A = [1, 2; 0, 1];
B = [4, 7; 4, 6];
X = AB
X =

    -4    -5
     4     6

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