1. 8.4 Matrix Operations Day 1 Thurs May 7 Do Now Solve X – 2y = -6 3x + 4y = 7

2. Matrices A matrix is an organization of numbers in a rectangular form

3. Matrices The rows of a matrix are horizontal The columns are vertical A matrix with m rows and n columns is said to be of order m x n The numbers in a matrix are called entries The main diagonal starts from the top left and travels down and to the right

4. Matrix Operations Matrix Addition and Subtraction Scalar Multiplication Matrix Multiplication

5. Matrix Addition and Subtraction Given Matrix A and B with the same order A + B = add corresponding entries A – B = subtract corresponding entries

6. Ex Find A + B for

7. Ex Find C – D for

8. You try Find A + B for

9. Additive Inverse The additive inverse of a matrix is obtained by replacing each entry with its opposite

10. Ex Find –A and A + (-A) given

11. Scalar Multiplication The scalar product of a number k and a matrix A is the matrix kA, obtained by multiplying each entry of A by the number k

12. Ex Find 3A and (-1)A for

13. Ex P.716

14. Matrix Multiplication When multiplying 2 matrices, there is a prerequisite that must be satisfied, or it cannot happen Matrix: Dimensions: The two inside dimensions must be equal, or the multiplication is not defined Note: Just because AB exists, doesn’t mean that BA also exists

15. Can we multiply these matrices? 1) 2) 3)

16. Multiplying Matrices To multiply, take the 1st row of matrix A and the 1st column of Matrix B – Multiply each corresponding element, and then add them together to get each new element

17. Ex Let Find 1) AB 2) BA 3) BC 4) AC

18. Closure Multiply AB given HW: p.720 #1-27 odds

19. 8.4 Matrix Operations Day 2 Fri May 8 Do Now Find AB given

20. HW Review: p.720 #1-27

21. Properties of Matrix Multiplication A(BC) = (AB)C A(B + C) = AB + AC (B + C)A = BA + CA Note that property 2 and 3 result in different matrices

22. Word problems When constructing a matrix from a word problem, the rows and columns should represent different types of the same thing (rows: types of cookies) (columns: amount of sugar)

23. Ex7 P.718

24. Matrix Equations We can write a system of equations into a matrix equation by making each column equivalent to a variable

25. Ex Write the following system into a matrix equation 4x + 2y – z = 3 9x + z = 5 4x + 5y – 2z = 1

26. Closure What must be true when multiplying matrices? Adding matrices? HW: p.720 #29-45 odds