evaluate matrix with respect

Hello I have a symbolic matrix lets say A=[a11,a12,a13;a21,a22,a23;a31,a32,a33] Then I need to solve the matrix with respect new variable that I defined v12=a21/a11; v13 = a31/a11; v23=a32/a22; a21=a21; a31=a13; a23=a32; E1 = 1/a11 E2=1/a22; E3=1/a33. I need to find matrix inv(A) but with respect v12, v13, v23, E1, E2, E3. I looked in the help menu but i can;t find any functions for it, Can anyone help me

[Oleg Komarov]

Not clear, I'm sorry.

[Andrew Newell]

Do you mean a21=a12?

Answer 1

[Andrew Newell]

Assuming you really mean a21=a12, you want to make A a symmetric matrix and then substitute for the six independent variables. The new variables can be solved by inspection to get the substitutions you need. You can do the substitutions first, then calculate the inverse:

A = sym('a%d%d',[3 3])
syms v12 v13 v23 E11 E22 E33
A = subs(A,{'a11','a22','a33','a21','a31','a32'},{1/E11,1/E22,1/E33,v12*E11,v13*E11,v23*E22})
A = subs(A,{'a12','a13','a23'},{A(2,1),A(3,1),A(3,2)})

EDIT: This is the output of the last command:

A =

[   1/E11, E11*v12, E11*v13]
[ E11*v12,   1/E22, E22*v23]
[ E11*v13, E22*v23,   1/E33]

EDIT: Now you can calculate the inverse:

inv(A)

I won't reproduce the answer, since it's pretty messy.