Practice!

Sample Problem

Find the determinant of

det(A)=

Solution

The determinant of A is the sum of the entries in ANY row or column of A multiplied by their respective cofactors. In this case, let’s choose row 1 because there is a zero entry in the second column of the first row. (We could also choose the second column, third column, and third row since they all have a 0 entry).

The determinant of

Since a12=0 à |A|=a11C11+a13C13

C11=(-1)1+1M11=M11=8

C13=(-1)1+3M13=M13=6

|A|=a11C11+a13C13=3(8)+1(6)=30