Inverse of a general matrix

[Snowslider]

Hello, please, how should I begin when I want to get an inverse matrix from this one... Thank you so much...

 

[Deleted member 4993]

Hello, please, how should I begin when I want to get an inverse matrix from this one... Thank you so much...

Try Gauss-Jordan elimination method.

 

[HallsofIvy]

There are a number of different ways to find the inverse of a matrix. I don't know, since you did not show any attempt of your own, what methods you have learned or are expected to use, but the simplest, I think is to write the identity matrix just to the right of the given matrix, then apply "row operations" to reduce the given matrix to the identity matrix while applying those same row operations to the identity matrix. That is the "Gauss-Jordan elimination method" that Subhotosh Kahn refers to.

 

[Deleted member 4993]

This particular matrix is kind of simple.

If you look at the bottom most row - you can factor out n and get 100000...0000 as the last row.

Then factor out (n-1) and get 1100000..0000 as the next to last row.

Thus you can factor out n! and be left with a very simple matrix.