Question

How can I partition a matrix into several smaller matrices to find unknown variables?

For example, given:

how can solve this problem by partitioning (splitting) a matrix 3×3 into smaller matrices (1×1 or other) to find the values of x, y, z and u?

Answer 1

In the new image, you isolate for the unknown matrix using some identities:

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

In Matlab:

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

Output:

ans =

    -4    -5
     4     6