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Working with Determinants
 
Evaluate the determinant:  


Enter the determinant:

Step 1:  Go to Matrix
                 (above the  x-1 key)

 

Step 2:  Arrow to the right to
             EDIT to allow for
             entering the determinant.
 

Step 3:  Type in the dimensions (size) of your determinant and enter the values (press ENTER).    
 


Evaluate the determinant:
Step 4:   Go to Matrix again.  Notice that your matrix (3x3) now appears showing it in residence.

  		Step 5:   Arrow to the right to
             MATH.  Choose
             #1: det ( 

  		Step 6:  The function det( will appear on the home screen waiting for a parameter (in this case, the name of the determinant to evaluate).
 
Step 7:   Go to Matrix again.  Choose [A] or whichever location holds your determinant.

. 		Step 8:  The name of the determinant's location will appear as the parameter.  Hit ENTER to see the evaluation.
 
Notice that it was necessary to make 3 trips to the Matrix key to accomplish this task.

 

Applications of Determinants


1.  Solve this system of equations using Cramer's Rule:
 		 2y + 3x = -1
4 = 2x - y
Line up:
3x + 2y = -1
2x -   y =  4		 Set up Cramer's Rule:
 Evaluate the determinants:
          		Answer:
  (1,-2)
 

2.   Find the area of a triangle with vertices A(6,1), B(1,2), and C(3,6).

Formula:  The area of a triangle having vertices (x1,y1), (x2,y2), and (x3,y3) is the absolute value of :

 		 Substitute values:
    		Calculate the answer:
     

 



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