solve system by converting a matrix to vector

how i can solve like this eqation:

Ax=b for x,

where A is 2(n-1)×2(n-1) matrix

and b is 2(n-1)×(n-1)matrix

and x=[u v]' is 2(n-1)×(n-1)matrix where u and v are (n-1)×(n-1) matrices

i tried to ues lsqr but i always got an error. I think that because b should be a vector andon also x should be one variable not two u and v.

so my qusetion is can i convert x and b to be as vector and how?

and if i can convert them then i have to change the size of A and make it larger than what its , i think about adding zeros, but it not works with me

Answer 1

[Torsten]

n = 4;
A = rand(2*(n-1),2*(n-1));
b = rand(2*(n-1),n-1);
x = A\b

x = 6×3

-0.2838 -5.2253 -6.4847 0.3891 3.3280 -7.6502 0.6037 3.2668 5.9517 -2.3993 -9.4441 3.3258 1.5573 4.1153 -0.2843 1.3017 3.6396 0.9060

u = x(1:n-1,:)

u = 3×3

-0.2838 -5.2253 -6.4847 0.3891 3.3280 -7.6502 0.6037 3.2668 5.9517

v = x(n:2*(n-1),:)

v = 3×3

-2.3993 -9.4441 3.3258 1.5573 4.1153 -0.2843 1.3017 3.6396 0.9060