# Calculating determinant by cofactors

1. Aug 2, 2006

### Bob

Show that evaluating the determinant of an n*n matrix by cofactors involves (n!-1) additions and $$\sum^{n-1}_{k=1}n!/k!$$multiplications.

What does it mean? how to do it? Help!!!

Last edited: Aug 2, 2006
2. Aug 2, 2006

### matt grime

Induction. You're trying to count the number of basic operations in expanding this (a necessary technique if one wants to estimate how long it will take on a computer). You can do this inductively since expanding by cofactors writes an nxn determinant in terms of n lots of (n-1)x(n-1) determinants.

3. Aug 3, 2006

### HallsofIvy

Staff Emeritus
As and example, to find the determinant
$$\left|\begin{array}{cc}a && b \\ c && d\end{array}\right|= ad- bc$$
$$\sum^{2-1}_{k=1}2!/k= \frac{2!}{1}= 2$$