Re: use of symbolic toolbox for the inverse of a matrix

[Jordi Gutiérrez Hermoso]

On 29 September 2011 11:47, george brida <address@hidden> wrote:
> Dear Octavers,
> I have the following matrix A:
> A(1,1)=T ;  A(1,2)=T*(T+1)/2  ;
> A(2,1)=T*(T+1)/2 ; A(2,2)= T*(T+1)*(2*T+1)/6
>
> I would like to find the inverse of this matrix in this general form.

The symbolic packge doesn't have symbolic matrices implemented yet.
This is how to do it in Sage instead:

    sage: t = var('t')
    sage: X = matrix([ [t, t*(t+1)/2], [t*(t+1)/2, t*(t+1)*(2*t+1)/6]])
    sage: X
    [                t                 1/2*(t + 1)*t]
    [    1/2*(t + 1)*t       1/6*(t + 1)*(2*t + 1)*t]

    sage: X.inverse()
    [-3*(t + 1)^2/(3*(t + 1)^2*t - 2*(t + 1)*(2*t + 1)*t) + 1/t
             6*(t + 1)/(3*(t + 1)^2*t - 2*(t + 1)*(2*t + 1)*t)]
    [6*(t + 1)/(3*(t + 1)^2*t - 2*(t + 1)*(2*t + 1)*t)
              -12/(3*(t + 1)^2*t - 2*(t + 1)*(2*t + 1)*t)]

HTH,
- Jordi G. H.