Matrices Matrix A matrix is a mathematical model

Matrices

Matrix �A matrix is a mathematical model that allows data to be represented �You can combine matrices together �Increase their value through scalar multiplication �Change the results through multiplication �Solve them for answers to linear equations �Get a numerical value to interpetation

Businesses �Businesses use matrices in a variety of ways �In manufacturing, they are used to get solutions to linear equations �In models, they are used to determine functionality for analysis of product design �In marketing, they are used to determine a value for a set of events

�In economics, they are used to make conjectures on what your opponent will do and assign a value to the outcome �Game theory is the strategy that uses this idea – it can be as simple as two choices for each person – 2 x 2 or as large as 16 x 16 (sixteen choices for what each person can do) �The ways to solve are limitless

Science �In science, they are used to assign the possible outcomes for genes �Pundit square: �Eye color outcome – Bb parent and Bb parent �B is dominant Type B b �b is recessive B b

Parts of a matrix �Matrix is made up of rows and columns �Rows are listed down the side �Columns are list across the top �You name the matrix by rows and columns �If a matrix has 2 rows and three columns then it is called: A 2 x 3

� �Rows columns Dimension for A is �A 12 is located in what row and what column?

Give the dimension of each matrix �A B C �A B �C D D

Scalar multiplication �Any number that is multiplied to all parts of a matrix �This changes the “size” of the value � 3 A – multiply all of matrix A by 3 �A = 3 A =

Example �A � 1. 2 A � 4. -B B C 2. -3 C D 3. 4 D

Combining matrices by Addition or Subtraction �In order to combine matrices by addition or subtraction they must have the same dimension �Which of the following can be combined? �A 2 x 3 B 3 x 2 C 2 x 2 D 1 x 5 E 2 x 3 F 3 x 2

Example �A � 1. A – C B C 2. A + B D 3. D + B

Solving for a missing part of a matrix �Set each place in one matrix equal to the same place in another matrix �Solve for the variable

Solve to make the matrices equivalent �Determine the values to make Matrix A = Matrix B �A B

Journal 1 �Name three ways that matrices are used in the real world. �Why do you think this format is useful?

Assignment 1 �Worksheet