0
$\begingroup$

With the following matrix where there are relations between different variables a,b,c,d, how can I instruct Mathematica to yield the answer only in terms of variables a and X

    d/(2 b) == X; (b + c)/(2b) == X; (e - b)/(2b) == X;

mat = FullSimplify[{{a - I ((b + c)/2), d}, {d, a - I ((e - b)/2)}}]
$\endgroup$
3
$\begingroup$
ClearAll["Global`*"]

Since there are only three equations for the relations, you can only eliminate three variables. In addition to a and X, e will also remain.

repl = Solve[{d/(2 b) == X, (b + c)/(2 b) == X, (e - b)/(2 b) == X},
   {b, c, d}][[1]]

(* {b -> e/(1 + 2 X), c -> (e (-1 + 2 X))/(1 + 2 X), d -> (2 e X)/(1 + 2 X)} *)

mat = {{a - I ((b + c)/2), d}, {d, a - I ((e - b)/2)}} /. repl // Simplify

(* {{(a + 2 a X - I e X)/(1 + 2 X), (2 e X)/(1 + 2 X)}, {(2 e X)/(1 + 2 X), 
  (a + 2 a X - I e X)/(1 + 2 X)}} *)
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.