How to Compute Determinants:
We define the determinant of a
matrix this way:
Then we use our definition of the determinant of a
matrix to define the determinant of a 
matrix:
In other words, we go across the first row of the matrix
, 
. We multiply each entry by the determinant of the matrix we get from by crossing out the row and column containing that entry. (Try this. If you take and cross out the row and column containing 
(the first row and the second column) you get the matrix 
; this was the matrix whose determinant we multiplied by in computing the determinant of .) Then we add and subtract the resulting terms, alternating signs (add the 
-term, subtract the -term, add the 
-term.)
