1. Section 10.2.1 – Operations with Matrices No Calculator By the end of this lesson you should be able to: Write a matrix and identify its order Determine if 2 matrices may be added, subtracted, or multiplied together Add, subtract, and multiply matrices

2. Matrix – an array (set) of numbers arranged in rows and columns Dimension of a Matrix – number of rows x number of columns 2 x 2 4 x 1 3 x 2 2 x 3 1 x 11 x 3 Write a matrix and identify its order

3. Addition of Matrices Dimensions MUST be the same for sum to exist Sum - DNE Determine if 2 matrices may be added together Add, and subtract multiply matrices

4. Subtraction of Matrices Dimensions MUST be the same for sum to exist Sum - DNE Determine if 2 matrices may be subtracted together

5. Scalar – a number SCALAR Multiplication (always works) Determine if 2 matrices may be multiplied together

6. MATRIX MULTIPLICATION 1.Order makes a difference…AB is different from BA 2.Number of columns in first matrix must equal number of rows in second matrix. (middle numbers match) 3.Answer will be number of rows in first matrix by number of columns in second matrix. (outside numbers) 2 x 11 x 2 Are the following matrix multiplications possible? 1 x 2 2 x 1 Determine if 2 matrices may be multiplied together

7. Are the following matrix multiplications possible? 3 x 2 NO 2 x 3 3 x 2 YES 3 x 2 2 x 3 YES 3 x 1 1 x 3 YES 2 x 2 YES 3 x 3 2 x 2 NO Determine if 2 matrices may be added, subtracted, or multiplied together

8. What is the dimension of the answer going to be? 3 x 2 NO 2 x 3 3 x 2 YES 3 x 2 2 x 3 YES 3 x 1 1 x 3 YES 2 x 2 YES 3 x 3 2 x 2 NO 2 x 2 3 x 3 2 x 2 multiply matrices

11. MATRIX MULTIPLICATION STEPS 1. Is the multiplication possible? (middle numbers match) 2. If yes, what is the dimension of the answer? (outside numbers) 4. “Multiply/Add” corresponding rows and columns 3. Create “blank” matrix. multiply matrices

12. Section 10.2.1 – Operations with Matrices No Calculator By the end of this lesson you should be able to: Write a matrix and identify its order Determine if 2 matrices may be added, subtracted, or multiplied together Add, subtract, and multiply matrices Homework: Pg. 733 #6, 8, 12 (Read directions, there are parts a – d) #28, 30, 32 (Read directions, there are parts a – c) #34 - 40 even 10 total problems, but with each part of the directions you end up doing 25 total problems.