A simultaneous linear equation with coefficients as variables

How can I solve a simultaneous linear equation in which the coefficients are variables?

[Torsten]

Include an example for what you mean.

Answer 1

[Matt J]

If the equations are,

A*X=B

then the roles of A and X are interchangeable and you can solve for A by doing,

A=B/X

Note, however that the usual requirement that you have at least as many equations as unknowns still applies if you hope to have a uniquely defined solution. This means that if A is MxN, then X must be NxP with P>=N and B must be MxP in order to solve for the M*N unknowns.

Answer 2

[John D'Errico]

I assume you mean simultaneous linear equations where the coefficients are parameters that are assumed to be fixed, and not estimated, but may not be known at time of solution. For example:

syms a x y

EQ(1) = a*x + 2*y == 3;
EQ(2) = x - y == 2;

xy = solve(EQ,[x,y])

xy = struct with fields:
    x: 7/(a + 2)
    y: -(2*a - 3)/(a + 2)

So simple enough. Or, we can convert the problem to a matrix form, like this:

[A,B] = equationsToMatrix(EQ,[x,y])

A = 

B = 

The solution now uses backslash.

xy = A\B

xy = 

Which is the same solution as found by solve.