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Matrix Operations, a la Shmoop. Gilligan Huffington the third had a great
earnings report in January and February. With everyone feeling pretty good about the
bullish market, and the economy doing better as a whole…
…people are spending money like money is growing on trees. Finally.
Being the great businessman that Gilligan is, he wants to project how well his company
will do in March and April all together. He estimates that, in March, customers will
probably buy half the amount of things they bought in January…
…but they will buy the same amount in April as they did in February.
Here's our data for how many full-price and discounted handbags, watches, and shoes he
sold in January and February... in matrix format.
Why aren't we using tables? Well actually, matrices are a good way to
organize our data when we want to perform operations with them...
…such as adding them or multiplying numbers to the data.
First, let's figure out what the March and April data looks like.
In March, Gilligan estimates that customers will probably buy half the amount they bought
in January… …so we can just take January's data and
multiply the matrix by one-half. This is called "MULTIPLYING BY A SCALAR",
where scalar is just another name for a number. In essence, we will just multiply each number
in the matrix by one-half, to get 9, 6, 5, 7, 2, and 3. Those numbers are, for Gilligan’s
purposes, in “millions.” In April, Gilligan estimates that customers
will buy the same amount in April as they did in February, so we can just keep February's
data the same. Gilligan wants to find the total of March
and April's data, so we'll have to add the two matrices.
Note that, because the dimensions of both of these matrices are the same, we can add
them. If they weren't, we wouldn't be able to.
To add two matrices, we can just add each corresponding pair of numbers.
We get 9 plus 8 equals 17, 6 plus 7 is 13, 5 plus 6 is 11, 7 plus 2 is 9, 2 plus 9 is
11, and 3 plus 4 is 7. Our final answer… 17, 13, 11, 9, 11, and
7. Looks like Gilligan's going to have another
great two months... In fact… he feels like he’s died and gone
to heaven… in a handbag.
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