1. Linear System of Simultaneous Equations Warm UP First precinct: 6 arrests last week equally divided between felonies and misdemeanors. Second precinct: 9 arrests - there were twice as many felonies as the first precinct. Write a system of two equations and find out how many felonies and misdemeanors occurred.

2. Sections 4.1 & 4.2 Matrix Properties and Operations

3. Algebra

4. Matrix A matrix is any doubly subscripted array of elements arranged in rows and columns enclosed by brackets.

5. Dimensions of a Matrix

6. Name the Dimensions

7. Row Matrix [1 x n] matrix

8. Column Matrix [m x 1] matrix

9. Square Matrix Same number of rows and columns Matrices of nth order -B is a 3 rd order matrix

10. The Identity

11. Identity Matrix Square matrix with ones on the diagonal and zeros elsewhere.

12. The Equal

13. Equal Matrices Two matrices are considered equal if they have the same dimensions and if each element of one matrix is equal to the corresponding element of the other matrix. = Can be used to find values when elements of an equal matrices are algebraic expressions

14. To solve an equation with matrices 1. Write equations from matrix 2. Solve system of equations Examples =

15. Linear System of Simultaneous Equations How can we convert this to a matrix?

16. Matrix Addition A new matrix C may be defined as the additive combination of matrices A and B where: C = A + B is defined by: Note: all three matrices are of the same dimension

17. Addition IfIf and then

18. Matrix Subtraction C = A - B Is defined by

19. Subtraction IfIf and then

20. Matrix Addition Example

21. Multiplying Matrices by Scalars

22. Matrix Operations

23. Matrix Multiplication Matrices A and B have these dimensions: Video [r x c] and [s x d]

24. Matrix Multiplication Matrices A and B can be multiplied if: [r x c] and [s x d] c = s

25. Matrix Multiplication The resulting matrix will have the dimensions: [r x c] and [s x d] r x d

26. A x B = C [2 x 2] [2 x 3]

27. A x B = C [3 x 2][2 x 3] A and B can be multiplied [3 x 3] [3 x 2][2 x 3] Result is 3 x 3

28. Inversion

29. Matrix Inversion Like a reciprocal in scalar math Like the number one in scalar math

31. Transpose Matrix Rows become columns and columns become rows