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

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The discussion centers on the challenges of finding the determinant of an nxn matrix efficiently. The professor advises against using Laplace expansion due to its time-consuming nature. The student expresses confusion about the lack of guidance in their textbook and struggles with the professor's request to use indices. They attempt to simplify the matrix by manipulating rows but are unclear on the proper method. Overall, the conversation highlights the need for clearer instruction on efficient determinant calculation techniques.
JoshW
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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.
 

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

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