CODEWITHSUNDEEP
wolfram-mathematica
Ling Yang
Ling Yang

Reputation: 11

Mathematica can not solve a symbolic matrix equation

I want to use mathematica to solve a matrix equation, and i wrote the following code:

ClearAll

PAII = {{xx, yy, zz, ww}} // MatrixForm
PAII = Transpose[PAII] // MatrixForm
SMatrix = {{p - 1, q, 0, 0}, {p, -1, q, 0}, {0, p, -1, q}, {0, 0, p, q - 1}} // MatrixForm
PAII.SMatrix // MatrixForm
Solve[PAII.SMatrix = PAII, {xx, yy, zz, ww}] // MatrixForm

varibles PAII = {{xx yy zz ww}} are what i want to solve

equation is PAII.SMatrix = PAII

And it shows the following errors:

enter image description here

It seems that the Transpose and dot product function does not work.

I do not know how to solve this problem. Asking for ur help!

I tried to write the matrix with actual values, and it does not show errors.

Upvotes: 0

Views: 460

Answers (1)

Bill
Bill

Reputation: 3977

MatrixForm makes a result that is pretty to look at, but cannot be used in calculations. It is possible to use () to show your pretty result and still be able to use the actual values for calculations

Mathematica internally handles some row versus column vectors.

Use == and not = inside equations that are given to Solve

Try

(PAII = {xx, yy, zz, ww})//MatrixForm
(PAII = Transpose[PAII])//MatrixForm
(SMatrix = {{p-1,q,0,0},{p,-1,q,0},{0,p,-1,q},{0,0,p,q-1}})//MatrixForm
(PAII.SMatrix)//MatrixForm
(Solve[PAII.SMatrix == PAII, {xx, yy, zz, ww}])//MatrixForm

which returns the solution

{{xx -> 0, yy -> 0, zz -> 0, ww -> 0}}

and see if that provides the solution that you want.

Upvotes: 0

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