ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

Multiplying Matrices 1142 Views


Share It!


Description:

Go forth and multiply... matrices.

Language:
English Language

Transcript

00:04

Multiplying Matrices, a la Shmoop. Jerry is a terrible lawn bowler and wasn't able to make the team. [Jerry running away from bowling balls]

00:11

However, everyone who did make the team felt a little sorry for him. [Jerry crying]

00:15

So they decided the least they could do was make him their errand boy. [Jerry looks unimpressed]

00:19

The men and women's teams have just turned in their equipment list for the season.

00:23

The coach tells Jerry that it costs 10 dollars per ball, two dollars per pin, and 20 dollars [Paper sheet of the costs]

00:29

per uniform.

00:31

What is the total cost of equipment for each team?

00:34

Well, we know that to find the total cost for each team, we'll need to multiply the

00:39

number of equipment by the cost.

00:42

Remember, that if we're going to perform operations with our data, we should put our data in matrix

00:47

format...with equipment numbers in one matrix and costs in another matrix. [Matrices of the values]

00:52

But before we can multiply two matrices, we need to make sure that the number of columns

00:57

in matrix A is the same as the number of rows in matrix B.

01:02

In this case, we have 3 columns in the first matrix, and 3 rows in the second one.

01:06

Checks out!

01:07

To multiply the two, we'll be doing something funky.

01:11

We'll multiply corresponding entries in the first row of matrix A and the first column

01:15

of B...then add.

01:18

So...the first entry in the matrix is 5 times 10 plus 20 times 2 plus 15 times 20. [Finger points to the entries in the matrix]

01:25

And the second entry is 6 times 10 plus 15 times 2 plus 14 times 20.

01:31

5 times 10 is 50, 20 times 2 is 40, and 15 times 20 is 300.

01:36

So 50 plus 40 plus 300 is 390, which gives the men's team total cost of $390 for their

01:43

equipment.

01:44

For the women's team...we have that 6 times 10 is 60; 15 times 2 is 30 and 14 times 20 [Total cost for the mens team written in a matrix]

01:49

is 280.

01:50

60 plus 30 plus 280 is 370...so the women's team total cost of equipment is 370 bucks. [The cost of the women's team is added to the matrix]

01:58

Notice that our ending matrix has dimensions of 2 by 1, which is also the row of matrix

02:05

A and column of matrix B. If he keeps up the good work Jerry may soon be

02:10

promoted to errand man... [Jerry cries and team mate rubs him on the back]

Up Next

Tangent Half-Angle Formula
1362 Views

Mosquitos need their caffeine, just like the rest of us. Wouldn't think zipping around and stinging people all day long sap your energy?

Related Videos

Matrix Operations
762 Views

Your one video for all things matrix operations.

Inverse Matrices
691 Views

Neo, we're not in the Matrix anymore.

Identity Matrices
870 Views

Identity matrices sound more organized than identity crises, at least.