What is the Most Efficient Method for Finding the Determinant of an nxn Matrix?

[JoshW]

Homework Statement

Shown In the picture. I went to the prof for help he said and i quote :" don't use laplas expansion to find the determinate, it will take you for ever."

Homework Equations

I don't even know how to do this. prof had no notes on this and Boas is a god awful book for learning anything.

The Attempt at a Solution

Add every row to the last row. 1/last row - every other row. then every row minus the last. but my prof wanted it solved with indices. I don't know what that is or how to apply it as it has never came up.

 

[tommyxu3]

Adding one row to another and eliminate the order of the matrix, which may help.