Skip to content Skip to navigation

OpenStax_CNX

You are here: Home » Content » Matrices Homework -- Multiplying Matrices II

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Advanced Algebra II: Activities and Homework"

    Comments:

    "This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Busbee's Math Materials display tagshide tags

    This module is included inLens: Busbee's Math Materials Lens
    By: Kenneth Leroy BusbeeAs a part of collection: "Advanced Algebra II: Activities and Homework"

    Click the "Busbee's Math Materials" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Matrices Homework -- Multiplying Matrices II

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides further sample problems which develop concepts related to multiplying matrices.

Just for a change, we’re going to start with…Professor Snape’s grade matrix!

Table 1
  Poison Cure Love philter Invulnerability
Granger, H 100 105 99 100
Longbottom, N 80 90 85 85
Malfoy, D 95 90 0 85
Potter, H 70 75 70 75
Weasley, R 85 90 95 90

As you doubtless recall, the good Professor calculated final grades by the following computation: “Poison” counts 30%, “Cure” counts 20%, “Love philter” counts 15%, and the big final project on “Invulnerability” counts 35%. He was able to represent each student’s final grade as the product of a row matrix (for the student) times a column matrix (for weighting).

Exercise 1

Just to make sure you remember, write the matrix multiplication that Dr. Snape would use to find the grade for “Malfoy, D.” Make sure to include both the two matrices being multiplied, and the final result!

I’m sure you can see the problem with this, which is that you have to write a separate matrix multiplication problem for every student. To get around that problem, we’re going to extend our definition of matrix multiplication so that the first matrix no longer has to be a row—it may be many rows. Each row of the first matrix becomes a new row in the answer. So, Professor Snape can now multiply his entire student matrix by his weighting matrix, and out will come a matrix with all his grades!

Exercise 2

Let’s try it. Do the following matrix multiplication. The answer will be a 3×1 matrix with the final grades for “Malfoy, D,” “Potter, H,” and “Weasley, R.”

[ 95 90 0 85 70 75 70 75 85 90 95 90 ] [ .3 .2 .15 .35 ] = [ 95 90 0 85 70 75 70 75 85 90 95 90 ][ .3 .2 .15 .35 ]=

OK, let’s step back and review where we are. Yesterday, we learned how to multiply a row matrix times a column matrix. Now we have learned that you can add more rows to the first matrix, and they just become extra rows in the answer.

For full generality of matrix multiplication, you just need to know this: if you add more columns to second matrix, they become additional columns in the answer! As an example, suppose Dr. Snape wants to try out a different weighting scheme, to see if he likes the new grades better. So he adds the new column to his weighting matrix. The first column represents the original weighting scheme, and the second column represents the new weighting scheme. The result will be a 3x2 matrix where each row is a different student and each column is a different weighting scheme. Got all that? Give it a try now!

Exercise 3

[ 95 90 0 85 70 75 70 75 85 90 95 90 ] [ .3 .4 .2 .2 .15 .3 .35 .1 ] = [ 95 90 0 85 70 75 70 75 85 90 95 90 ][ .3 .4 .2 .2 .15 .3 .35 .1 ]=

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks