Thread: Need help and finding the inverse of this matrix.

Not sure whether to post this on the Linalg forums or the DE forums but I'm having trouble finding the inverse of a matrix needed to solve a system of non-HDEs.

Here's the matrix in maple.


Now I'm wondering how you can reduce the first matrix to the identity matrix in order to get it's inverse (the second matrix)? Since you can only use scalar multiplication of rows, row switching and scalar multiplication of one row + another row as row operations while this matrix is composed of exponential functions.

just treat e^t as a scalar (it is a scalar-valued function). multiplying a row (say the 2nd) by e^t, for example, is just multiplying by the matrix:

[1 ..0. 0]
[0 e^t 0]
[0 ..1. 0]

(in other words, the field of scalars is actually some field of functions. these things exist).

Thanks alot, just crunched it out just now by treating e^t as a scalar and the matrices match.