1. Matrix Operations
Chapter 4, Sections 1, 2, 3

2. What is a matrix?
A matrix is a rectangular arrangement of numbers in rows and columns.
Rows run horizontal.
Columns run vertical.
Each value in the matrix is called an element.
The dimensions of a matrix are stated “m x n” where “m” is the number of rows and “n” is the number of columns.

3. Special Matrices
Some matrices have special names because of what they look like:
Row matrix – has only one row
Column matrix – has only one column
Square matrix – has the same number of rows and columns
Zero matrix – contains all zeros

4. Equal Matrices
Two matrices are considered equal if they have the same number of rows and columns (the same dimensions) and all their corresponding elements are exactly the same.

5. Examples

6. Matrix Addition/Subtraction
Matrices can be added or subtracted if they have the same dimensions.
To add or subtract matrices – add or subtract the corresponding numbers.

7. Example
Go over examples of adding and subtracting matrices before going to the next slide.

8. Scalar Multiplication
Matrices can be multiplied by a number (called a scalar) – to do this, multiply each element of the matrix by the scalar.
This is like distributing a number.

9. Example
Do some examples of scalar multiplication before going to the next slide

10. Examples

11. Matrix Properties
A+B=B+A
(A+B)+C=A+(B+C)
c(A+B)=cA+cB

12. Matrix Multiplication
Matrices can be multiplied only if the number of columns in the first matrix is the same as the number of rows in the second matrix.
Matrix multiplication is NOT commutative, order matters!
2 columns
2 rows

13. How to multiply matrices:
To multiply matrices – go row by column
Take the numbers in the first row of matrix 1, multiply each element in that row by its corresponding element in the first column of matrix 2, add these products.

14. Matrix Multiplication
The dimensions of the product is the number of rows of matrix 1 by the number of columns of matrix 2. __
3 x 3
3 x 2
2 x 3 __ __

15. Example
3 x 2
2 x 1
Make sure students understand where the numbers are coming from, do some examples before going on to the next slide.

16. Examples

17. Matrix Properties (AB)C=A(BC) C(AB)=A(cB)=(cA)B C(A+B)=CA+CB
(A+B)C=AC+BC
AB is not the same as BA ***

18. Matrices in the Calculator
To enter a matrix:
2nd matrix
Go over to edit, press enter
Type the number of rows, enter, number of columns, enter
Type the elements of the matrix starting with row 1, column 1, press enter after each number
2nd quit to “save” the matrix

19. Matrices in the calculator
To perform operations:
Enter the matrices
2nd matrix, enter on first matrix
+ , – , or *
2nd matrix, enter on second matrix
Press enter to get the sum, difference, or product
For scalar multiplication, type the scalar then do 2nd matrix and enter on matrix, press enter for answer

20. Matrices in the calculator
ALL matrix operations can be done in the calculator!
Make sure students can put matrices in calculator and can perform operations.

21. Homework 4-1 in workbook 4-2 in workbook 4-3 in workbook EXIT SLIP:
1-3, 4, 10, 14-16
4-2 in workbook
7-12
4-3 in workbook
1-6, 15-18
EXIT SLIP:
NCSCOS Goal 1.04 Handout