20260202

In R2022b MATLAB or later

(1) Test whether symbolic MATLAB is installed. Start MATLAB and do commands:

a = [1 2 ; 3 4]
b = [4 ; 5]
syms x y
eqn = a * [x ; y] == b
solu = solve([eqn], [x, y])
solu.x
solu.y

(2) For bigger square matrices we may define:

badA = [1 2 3 ; 4 5 6 ; 7 8 9]
det(badA)
badA^(-1)
A = sym([1 2 3 ; 4 5 6 ; 7 8 9])
and B = sym([6 ; 15 ; 24])
det(A)
A^(-1)
syms x y z
eqn = A * [x ; y ; z] == B
solu = solve([eqn], [x, y, z])
solu.x
solu.y
solu.z

(3) In (2) still only one solution [0;3;0], MATLAB ignores kernel [1;-2;1]
HOWEVER, there is the nullspace operator and the range operator
null(A) (gives orthogonal basis)
colspace(A) (gives orthogonal basis)
So try:

null(A)
colspace(A)