Bell Ringer: 11/3/14 What is an irrational number? A real number that cannot be written as a simple fraction or whole number - the decimal goes on forever without repeating.

Unit 2 Sec. 1: Intro to Matrices I will learn how to write and use operations with matrices.

Intro to Matrices Applications Life Expectancy Pricing Advertising Manufacturing Credit Card Security Encoding/Decoding Messages Investment Programing-Video Games Ranking Teams- NCAA, NFL, NBA, FIFA

Intro to Matrices INTRO TO MATRICES A matrix is described by its ______________________: __________________ x ________________ Dimensions Rows Columns R O W S 𝐴= 8 −2 5 6 3 −3 7 11 −12 5 6 −15 Dimension: _____x___ 3 4 COLUMNS Elements The values/variables inside of a matrix are called the ______________________.   𝑎 𝑟𝑜𝑤 𝑥 𝑐𝑜𝑙𝑢𝑚𝑛 Using the matrix above, find the values for each of the following elements. 𝑎 23 = 𝑎 31 = 𝑎 33 = -3 7 -12 2nd 𝑟𝑜𝑤 3rd 𝑐𝑜𝑙𝑢𝑚𝑛

Organizing a Matrix

Operations with Matrices   Matrices can be added or subtracted if and only they have _____________ _______________. Find each of the following for 𝐴= −3 4 6 5 𝐵= 7 1 −3 0 𝐶= 3 5 6 −1 −2 6 𝐷= −5 −5 𝐸= −1 5 Same Dimensions 2 x 2 2 x 2 2 x 3 2 x 1 1 x 2 Example 1 A + B = −3 4 6 5 + 7 1 −3 0 = + + + + =   -3 4 6 5 7 1 -3 0 2 x 2 + 2 x 2

  Example 2 A - B = −3 4 6 5 − 7 1 −3 0 = − − − − = Example 3 A + D = −3 4 6 5 + −5 −5 = Example 4 2B = 2 7 1 −3 0 = 2 2 2 2 = -3 4 6 5 7 1 -3 0 2 x 2 - 2 x 2 Impossible 2 x 2 + 2 x 1 1 -3 0

  Example 5 2A-3B = 2 −3 4 6 5 – 3 7 1 −3 0 = 2 2 2 2 - 3 3 3 3 -3 4 6 5 7 1 -3 0 = - -6 8 12 10 21 3 -9 0

Assignment p. 175 #2,3,7,8,10,12,13

Bell Ringer: 9/3/15 If Matrix A= 3 2 4 5 and Matrix B = −5 1 −4 7 Perform the following operations: A + B 3B 2A-B

Answers to Assignment 2. 3 −5 7 3. Impossible 2. 3 −5 7 3. Impossible 7. −90 54 −12 −18 −36 66 −84 12 −24 48 60 −162 10. impossible 12 and 13. See Ms. Justus for answers

Multiplying Matrices In order to be able to multiply matrices, the number of columns from the first matrix must match the number of rows from the second matrix. The resulting size of the matrix will be the number of rows from the first matrix X the number of columns from the second matrix. Ex: A2x3 * B3x2 = 2 x 2 Ex: A3x2 * B3x2 = impossible

Instructions for Storing Matrices in a Graphing Calculator 1. Press 2nd button, then 𝑥 −1 button. This will bring you to the Matrix editing/storing screen. 2. Use directional arrows to highlight EDIT. Then choose a matrix to edit (I start with 1: )  3. Determine the size of your matrix and enter it in the dimensions at the top of the screen. Always press ENTER after pressing a value. 4. Once you have the correct dimensions of your matrix, begin entering your values in the matrix. Always press ENTER after each value, and the matrix fills in row first, then moves to the next row until all values are entered. 5. If you have more than one matrix to enter, repeat steps 1-4.

Instructions continued… 6. Once all matrices have been entered, press 2nd MODE, which gives you a clear screen to begin your calculations. 7. To use operations with matrices, press 2nd, then press 𝑥 −1 . Now you will choose which matrix you need by pressing the corresponding number in the list, or you can use the directional arrows, highlight the matrix you need and press ENTER. Use the correct operators and repeat the process to choose the appropriate matrices for the problem. 8. When you have finished entering the problem, press ENTER and it will give you a matrix answer if the answer exists. Write it exactly as it looks in the calculator. If you get an ERROR message, that means that either the problem is impossible to answer or there has been an entry mistake. Ask Ms. Justus for clarification.

Assignment P. 184 #15-17, 23,25,28,35