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

 From: george brida Subject: Re: use of symbolic toolbox for the inverse of a matrix Date: Fri, 30 Sep 2011 00:56:57 +0200

Dear friends,
thank you very much.

2011/9/29 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.