# Matrices

In the Real World

# At a Glance - In the Real World

Let's say you're working at A & F in the mall. You're in charge of shirts, because your manager thinks you have real promise. Don't let her down!

First, you're doing an inventory of red polo shirts. There are two kinds, with a logo and without a logo, and you have some of each kind in each of three sizes: small, medium, and large. You count them up as follows:

With logo: 3 small, 5 medium, 4 large
Without logo: 2 small, 4 medium, 6 large

You can enter your data into a matrix to keep track of those pesky shirts, where "with logo" is row one, "without logo" is row two, small is column one, medium is column two, and large is column three:

Since you're so amazing at inventory, you go ahead and count the blue polo shirts too:

With logo: 0 small, 7 medium, 1 large
Without logo: 3 small, 3 medium, 0 large

And the blue shirt matrix looks like this:

Naturally, your manager wonders how many shirts with logos there are in either color for each size. No problem! You've got it all laid out, matrix-style.

#### Example 1

 Let's say you're a big, BIG fan of Barry Manilow. Don't worry, we won't say it to anyone else. You have a collection that consists of 8 vinyl records, 6 eight-track tapes, 7 cassettes, and 3 CDs. You want to place the data about your collection into a matrix. What would that matrix look like?

#### Example 2

 Let's say we want to be more detailed about our Manilow Mania. We want to list in a matrix how many of each "Greatest Hits" (1978) and "Ultimate Manilow" (2004) albums we have. Of the 8 records, there are 5 "Greatest Hits" and 3 "Ultimate Manilow." For eight-tracks it's 4 and 2, for cassettes it's 2 and 5, and for CDs it's 1 and 2.

#### Example 3

 Finally, let's suppose we bought some of each of these works on eBay and some at Julio's Retro Wonderland, and for some reason, this matters to us. For sanity's sake, let's use this shorthand: G = Greatest Hits, U =Ultimate Manilow, E = eBay, and J = Julio's place. Here are our lists:Matrix E (our eBay purchases)Vinyl records: 3G, 3U8 tracks: 1G, 1UCassettes: 2G, 3UCDs: 1G, 0UMatrix J (our Julio's bargains)Vinyl records: 2G, 0U8 tracks: 3G, 1UCassettes: 0G, 2UCDs: 0G, 2UWhat does matrix E look like? How about matrix J?

#### Exercise 1

Create a matrix for the following data:

The forecast this week is as follows: Monday, a high of 76 degrees and a low of 40 degrees; Tuesday, a high of 71 degrees and a low of 43 degrees; Wednesday, a high of 69 degrees and a low of 40 degrees; Thursday, a high of 66 degrees and a low of 40 degrees; and Friday, thanks to the incoming meteor, a high of 178 degrees and a low of 165 degrees.

#### Exercise 2

There are three kinds of cookies for sale: lemon, chocolate, and lingonberry. There are 24 lemon cookies, 30 chocolate cookies, and 5 lingonberry cookies, since no one likes them. How do we represent this data in matrix form?

#### Exercise 3

We're looking at rental prices in three areas for apartments with one bedroom, two bedrooms, and three bedrooms. The average prices in Funky Town are as follows: for one bedrooms it's \$500, for two bedrooms it's \$800, and for three bedrooms it's \$1100. The average prices in Squalorville are as follows: for one bedrooms it's \$450, for two bedrooms it's \$900, and for three bedrooms it's \$1300. The average prices in Uptighton are as follows: for one bedrooms it's \$900, for two bedrooms it's \$1200, and for three bedrooms it's \$1600. Matrix that.