Message Boards Message Boards


Using CoefficientArrays to Invert simultaneous equations

Posted 3 months ago
2 Replies
2 Total Likes

The table obtained via the CoefficientArrays command of a list of vector equations does not seem to result in 3x3 Matrix as the coefficients of the original simultaneous equations.

I tried using LinearSolve to invert the simultaneous equations, and I faced the same issue. `(Deformation Equations)

X = {X1, X2, X3};
x = {x1, x2, x3};
Eulerian = {e^-\[ScriptT]*x1 + 0*x2 + (e^-\[ScriptT] - 1)*x3, 
  0*x1 + x2 + (e^-\[ScriptT] - e^\[ScriptT])*x3, 0*x1 + 0*x2 + x3}
CoefficientArrays[Eulerian, {x1, x2, x3}]
Normal[%] // MatrixForm
Take[%, {2}] // MatrixForm
q = Flatten[%, 1] (* q is the Coefficients Matrix of x *)
q // MatrixForm
qInv = Inverse[q] // MatrixForm (* Eulerian in terms of q *)
x = qInv . X(* Lagrangian Form *)

(* Velocity Vector Field*)
v = D[x, \[ScriptT]] // MatrixForm(* Material derivative*)`
2 Replies

A couple things: 1) When you do this:

m = {{1,2},{3,4}}//MatrixForm

m is no longer a matrix, it is a "Form" and


will not operate as you might expect. 2) It is much easier to debug if you put your input into separate Input cells and evaluate one at a time.

I've rewritten things here:

X = {X1, X2, X3};
x = {x1, x2, x3};

Eulerian = {e^-\[ScriptT]*x1 + 0*x2 + (e^-\[ScriptT] - 1)*x3, 
  0*x1 + x2 + (e^-\[ScriptT] - e^\[ScriptT])*x3, 0*x1 + 0*x2 + x3}

I suspect you want Exp[..] or E^(..) instead of e? It is a good habit to define your own symbols with lower case letters.

ca = CoefficientArrays[Eulerian, {x1, x2, x3}] (*same as CoefficientArrays[Eulerian, x]*)

(nca = Normal[ca]) // MatrixForm 

notice that the = is done before the output is turned into a "Form"

Also, you can just do this directly:



(tnca = Take[nca, {2}]) // MatrixForm (*do you mean nca[[2]] here? tnca has dimensions {1,3,3}, and nca[[2]] has dimensions {3,3} I'll keep working as though Take is what you want*)

q = Flatten[tnca, 1]

q has dimensions {3,3} now

qInv = Inverse[q]

You are redefining x here.

x = qInv . X

And this gives an expression:


Thanks, Craig Very helpful, and it fixed my code!

Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
or Discard

Group Abstract Group Abstract