Solving System of linear equations of the Matrix of Matrices Form

How can I solve this Matrix A which contains Matrices ? values can be random, I just need the method to solve for A*X = B

Answer 1

[Walter Roberson]

You will need to write the code yourself. Mupad has no built in mathematical functions for matrices of matrices.

[Maria Saleem]

Problem is , I dont know the method , using which i can solve such system of matrices

[Walter Roberson]

First you need to define what the operations even mean.

You have 2 x 2 sub-matrices. Normal linear algebra of * operator on

A11 A12  * x1
A21 A22    x2

would look like

A11*x1 + A12*x2
A21*x1 + A22*x2

Your B is 2 x 1 scalars. If x1 is n1 x m1, and x2 is n2 x m2, then we deduce that (2 x 2) * (n1 x m1) + (2 x 2) * (n2 x m2) = scalar . The * operator cannot work unless the inner dimensions match, so we deduce that n1 and n2 must be 2 -- (2 x 2) * (2 x m1) + (2 x 2) * (2 x m2) = scalar. The addition cannot work unless m1 = m2, so (2 x 2) * (2 x m) + (2 x 2) * (2 x m) = scalar. The (2 x 2) * (2 x m) is going to be 2 x m result, so you are adding a pair of 2 x m values, and the result must be 1 x 1. This is impossible in normal linear algebra. Therefore you must be using a different meaning of solving for A*X = B than standard linear algebra. You need to strictly define what your operations mean, and prove that they are consistent before you get very far.