Howard S. Hamilton ........................................................................................hsh2760
Week 11 ...........................................................................................................7-1-14
http://www.cs.tamu.edu/people/hamilton/math-311/week11/7-1-14.html

Calculate the determinate of the following matrix:    

Solution:

The determinate of this matrix may be calculated using the cofactor expansion algorithm where:

where A_jk is the matrix obtained by omitting the row and column
of A containing a_jk^.

Using this method, we expand the 4x4 matrix into a sum of 4 determinates of 3x3 matrices:

1*det -3*det+0* det+0* det

Since the last matraces will be zero, we can exclude them from our calculations.

Calculating the first two determinates using the same method:

det = 0 - 5* det + 7 *

det = 0 - 5*(-32)  + 7 *(-24)

det = -8

Additionally

det = 0 - 5* det + 7 *

det = 0 - 5*(-16) + 7*(-12)

det = -4

Therefore:

1*(-8) -3*(-4) = 4

Which is the answer we seek.