1. MATRICES
MATRIX OPERATIONS

2. Matrix Determinants
A Determinant is a real number associated with a matrix. Only SQUARE matrices have a determinant.
The symbol for a determinant can be the phrase “det” in front of a matrix variable, det(A); or vertical bars around a matrix, |A| or

3. Matrix Determinants
To find the determinant of a 2 x 2 matrix, multiply diagonal #1 and subtract the product of diagonal #2.
Diagonal 1 = 12
Diagonal 2 = -2

4. Matrix Determinants
To find the determinant of a 3 x 3 matrix, first recopy the first two columns. Then do 6 diagonal products.
-20
-24 36 18 60 16

5. Matrix Determinants = (-8) - (94) = -102
The determinant of the matrix is the sum of the downwards products minus the sum of the upwards products.
-20
-24 36 18 60 16
= (-8) - (94) = -102

6. Area of a Triangle
The area of a triangle can be written using the 3 vertices:
The ± makes the area always positive.
(x1, y1)
(X2, y2)
(X3, y3)

7. (2, 7)
Example
(-2, -1)
(6, 1) - - 8
(-56) = 28 sq. units -

8. Cramers Rule for a 2x2 System
ax+by=e
cx+dy=f
The coefficient matrix is A:

9. Cramers Rule for a 2x2 System

10. Cramers Rule for a 2x2 System

11. Cramers Rule for a 3x3 System

12. Cramers Rule for a 3x3 System
ax+by+cz=j
dx+ey+fz=k
gx+hy+iz=l
z =

13. Cramers Rule for a 3x3 System

14. Cramers Rule for a 3x3 System

15. Cramers Rule for a 3x3 System

16. Cramers Rule for a 3x3 System