**Organizing Data Using Matrices**

In robotics, matrices are the key concept for the movement of the robot. The robot's movement is programmed with the calculations of matrices' rows and columns.

Some who survey people (surveyors) on account of population or as simple as "your favorite type of..." can use matrices on a daily basis

In robotic engineering matrices are used to determine which action the robot takes next and how it moves around

Many geologists make use certain types of matrices for seismic surveys

Citations

"Application of Matrices in Real Life." Application of Matrices in Real Life. N.p., n.d. Web. 15 May 2014.

"What Are Matrices Used for." - Ask.com. N.p., n.d. Web. 15 May 2014.

"Working with Matrices." Working with Matrices. Web. 20 May 2014.

Think-Pair-Share

In their class tests, Robert scored 85 in Math, 75 in Geography, and 80 in History, while Kathy scored 70 in Math, 80 in Geography, and 75 in History. Let the first and second rows represent the scores of Robert and Kathy respectively. Also, let the first, second, and third columns represent the scores for Math, Geography, and History respectively. Which of the following represents their scores in matrix form?

What are Matrices?

A Matrix (matrices in plural) is an ordered rectangular array of numbers. The array can also contain symbols and/or expressions. Every individual number, symbol or expression in a matrix is called an element or an entry. Rows are horizontal and columns are vertical. Each number in the matrix is called an element.

The prices of things at two different supermarkets are different in different cities. Toilet paper in Duluth, Minnesota costs $3.99 per package while toilet paper in NYC costs $8.95 per package. In Duluth, toothpaste costs $1.95 per tube, while in NYC, it costs $5.25 per tube.

This data can be encoded in the following grocery matrix:

Real World Word Problems

What did you get?

Think-Pair-Share... IN DETAIL

Now that you have your matrix, you can figure out many different ideas. For example, you can pick it apart and find out what a specific person got on a certain topic. Or if they got the same grades more then once, you can multiply the matrix by that amount!

Careers Involving Matrices

Analysts research what items consumers want, what prices consumers are willing to pay, and how well competitors’ products are selling. The data gathered can also be used to predict future sales. The data can be organized into matrices to make working with data easier.

Statisticians work in many different areas such as analyzing data collected from experiments in science, determining the number of households who watch a given television show, analyzing surveys measuring unemployment for the government, and compiling statistics on sporting events. Statisticians design many surveys and set the procedures to be followed from how to sample the population to the questions being asked. The data can be organized into matrices. Then, using computers, the data can be analyzed and summarized.

A question you may have is ,"How will this help me in the real world?" Well, we have an answer for you!

Everyday Examples

Grading done by teachers:

A class can be modeled as a matrix (M) where the rows are students and the columns are grades on various assignments, one column for each assignment. A column vector (W) has the weights of how much each assignment counts towards your final grade. The final grades for the entire class are computed by the matrix product M x W.

Baseball:

A table of baseball batting averages is an example of a matrix. The first column is typically a list of each ball player's name on the team. The second column is usually made up of each corresponding player's batting average.

From making matrices from data like this you can benefit from many things. With baseball you can compare your and your teammates averages. Then you will be able to see what you can do better just like when the teacher grades papers. You will get to see what your grade is and where you went wrong.

Now let's analyze the details. Look at your matrix and write down...

1) What was Robert's History score?

2) What was Kathy's Math score?

3) Who had the higher mean out of the two kids?

You have 1 minute!

You have 2 minutes!