Skip to content Skip to navigation Skip to collection information

OpenStax-CNX

You are here: Home » Content » Advanced Algebra II: Teacher's Guide » Multiplying Matrices II (the full monty)

Navigation

Table of Contents

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 collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "This is the "teacher's guide" 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 […]"

    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 collection is included inLens: Busbee's Math Materials Lens
    By: Kenneth Leroy Busbee

    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.
 

Multiplying Matrices II (the full monty)

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

Summary: The second part in a teacher's guide to multiplying matrices.

This time, you’re going to have to lecture. You are going to have to explain, on the board, how to multiply matrices. Probably a good 20 minutes (half the class) dedicated to showing them that this row goes over here to this column, and then we go down to the next row, and so on. Get them to work problems at their desks, make sure they are cool with it. You can also refer them to the “Conceptual Explanations” to see a problem worked out in a whole lot of detail.

Two things to stress:

  1. Keep doing the visualization of a row (in the first matrix) floating up and twisting to get next to a column (in the second matrix). If the two do not line up—that is, they have different numbers of elements—then the multiplication is illegal.
  2. Matrix multiplication does not commute. If you switch the order, you may turn a legal multiplication into an illegal one. Or, you may still have a legal multiplication, but with a different answer. AB AB and BA BA are completely different things with matrices.

You may never get to the in-class assignment at all. If you don’t, that’s OK, just skip it! However, note that the in-class assignment is built on one particular application, which is showing how Professor Snape can do just one matrix multiplication to get the final grades for all his students. This exercise is one of the few applications I have for matrix multiplication.

Homework:

“Homework—Multiplying Matrices II”

#4 is important for a couple of reasons. First, of course, by using variables, it forces them to do the work manually even if they have figured out how to do it on a calculator. More importantly, it continues to hammer home that message about what variables are—you can solve this leaving x x, y y, and z z generic, and then you can plug in numbers for them if you want.

#5 and #7 set up the identity matrix; #6 sets up using matrices to solve linear equations. You don’t need to mention any of that now, but you may want to refer back to them later. I don’t want them to think of [ I] [I] as being defined as “a diagonal row of 1s.” I want them to know that it is defined by the property AI=AI=A AI AI A , and to see how that definition leads to the diagonal row of 1s. #7 is the key to that.

Collection Navigation

Content actions

Download:

Collection 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 ...

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:

Collection 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

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