Section 4.3: Determinants
note: you can only find determinants for square matrices, which means
that the number or rows has to be equal to the number of columns.)
When given a 2 by 2 matrix, you multiply it's cross numbers          
and then subtract them from one another. For the following example, this          
of the equation:

(ad) - (bc) (a multiplied by d) minus (b multiplied by c)
When given a 3 by 3 matrix you can use the diagonal method of multiplying       
numbers and then subtracting them. 
When looking at a 3 x 3 matrix, expand       
it so that you have rewritten the first 2 columns again after the 3rd         
column so that you now have 3 rows and 5 columns. 
When looking at this example; think of the equation as: 

[ (aei) + (bfg) + (cdh) ] - [ (gec) + (hfa) + (idb) ] 
This can apply to everyday life in geometry when trying       
to find the area of the triangle. When you are given 3 coordinates of         
a triangle, you can use the matrices method to find the area. For Example: 
      
The area of a triangle with vertices A(x,y) B(v, w) C(s,t) is: AREA =   
      
 + or - 1/2 Area is equal to plus or minus (this would be the last step)       
half the determinant of your coordinates. First step is to find 
your determinant from the coordinates using the diagonals method. 
Then, you divide this number by 2. If it is negative, place the 
negative sign in front of it to make it positive 
(because you cant have a negative area) and that is        
the area of the triangle. 


You Try: 
1) Find the area of a triangle who's     
     points are (4,2) (1,-2) (3,-4) 
2) Find the area of a triangle who's points        
  are (-3, 4) (4,2) (1,-2) 
3) Find the area of a trapezoid who's points        
  are (2,3) (7,4) (5,0) (0,0) 
(hint, find 2 triangles and add them together)          


Answers: 
1) 7 
2) 17 
3) 33/2