1. Finding the Area of a Triangle

2. Find the area of the Triangle 121 5 91 951 Use a Determinant

3. Find the area of the Quadrilateral Divide into two triangles

4. Find the area of the Quadrilateral -321 3 91 951 The top triangle

5. Find the area of the Quadrilateral 951 1 -51 -321 The bottom triangle

6. Find the area of the Quadrilateral

7. Multiplying Matrices

8. Standard MM3A4. Students will perform basic operations with matrices. a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology. b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology. c. Examine the properties of matrices, contrasting them with properties of real numbers.

9. In order to multiply matrices... A B = AB m x nn x pm x p Can you multiply? What will the dimensions be? 2 x 33 x 4 AB 5 x 35 x 2 2 x 4 Not possible Ex 1. AB AB AB

10. How to multiply... ac = ad 2 x 11 x 22 x 2

11. How to multiply... ac = ad 2 x 11 x 22 x 2 bcbd

12. Ex. 1

13. How to multiply... ag = +bi+ckah+bj+cm 2 x 33 x 2 2 x 2

14. How to multiply... ag = +bi+ck dg+ei+fk ah+bj+cm dh+ej+fm 2 x 33 x 2 2 x 2

15. Ex. 2 -1(4)+5(6) 5(-3)+2(8)5(4)+2(6) 0(4)+-4(6)0(-3)+-4(8) -1(-3)+5(8) -4+ 30 -15+ 1620+12 0+ -240+ -32 3+ 40 26 1 32 -24 -32 43 =

16. Ex. 3 -16+ 1 0- 4 -12+2 0- 2 -15 - 4-2 -10 = Find AB

17. Ex. 4 Find BA

18. Ex. 5

19. 2 X 3 3 X 3 Ex. 6

20. Ex. 7

21. What are your questions?

22. Assignment Handout