# Connexions

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

### 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?

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

#### 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

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

"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 to display tags associated with this content.

#### Also in these lenses

• Busbee's Math Materials

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 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 -- Homework: Multiplying Matrices II

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

Summary: This module provides further practice problems related to multiplying matrices.

## Exercise 1

Matrix [A][A] is 12341234 size 12{ left [ matrix { 1 {} # 2 {} ## 3 {} # 4{} } right ]} {}. Matrix [B][B] is 56785678 size 12{ left [ matrix { 5 {} # 6 {} ## 7 {} # 8{} } right ]} {}.

• a. Find the product ABAB.
• b. Find the product BABA.

## Exercise 2

Multiply.

2 6 4 9 5 8 2 5 4 7 3 4 6 9 8 4 2 0 2 6 4 9 5 8 2 5 4 7 3 4 6 9 8 4 2 0 size 12{ left [ matrix { 2 {} # 6 {} # 4 {} ## 9 {} # 5 {} # 8{} } right ] left [ matrix { 2 {} # 5 {} # 4 {} # 7 {} ## 3 {} # 4 {} # 6 {} # 9 {} ## 8 {} # 4 {} # 2 {} # 0{} } right ]} {}

## Exercise 3

Multiply.

2 5 4 7 3 4 6 9 8 4 2 0 2 6 4 9 5 8 2 5 4 7 3 4 6 9 8 4 2 0 2 6 4 9 5 8 size 12{ left [ matrix { 2 {} # 5 {} # 4 {} # 7 {} ## 3 {} # 4 {} # 6 {} # 9 {} ## 8 {} # 4 {} # 2 {} # 0{} } right ] left [ matrix { 2 {} # 6 {} # 4 {} ## 9 {} # 5 {} # 8{} } right ]} {}

## Exercise 4

5 3 9 7 5 3 2 7 5 x y z 5 3 9 7 5 3 2 7 5 x y z size 12{ left [ matrix { 5 {} # 3 {} # 9 {} ## 7 {} # 5 {} # 3 {} ## 2 {} # 7 {} # 5{} } right ] left [ matrix { x {} ## y {} ## z } right ]} {}

• a. Multiply.
• b. Now, multiply 53975327521055397532752105 size 12{ left [ matrix { 5 {} # 3 {} # 9 {} ## 7 {} # 5 {} # 3 {} ## 2 {} # 7 {} # 5{} } right ] left [ matrix { 2 {} ## "10" {} ## 5 } right ]} {}—but not by manually multiplying it out! Instead, plug x = 2 x=2, y = 10 y=10, and z = 5 z=5 into the formula you came up with in part (a).

## Exercise 5

Multiply.

1 2 3 4 5 6 7 8 9 1 0 0 0 1 0 0 0 1 1 2 3 4 5 6 7 8 9 1 0 0 0 1 0 0 0 1 size 12{ left [ matrix { 1 {} # 2 {} # 3 {} ## 4 {} # 5 {} # 6 {} ## 7 {} # 8 {} # 9{} } right ]` left [ matrix { 1 {} # 0 {} # 0 {} ## 0 {} # 1 {} # 0 {} ## 0 {} # 0 {} # 1{} } right ]} {}

## Exercise 6

3 [ 3 -2 6 3 ] [ x y ] = [ 9 -3 ] 3[ 3 -2 6 3 ][ x y ]=[ 9 -3 ]

• a. Find the x x and y y values that will make this matrix equation true.
• b. Test your answer by doing the multiplication to make sure it works out.

## Exercise 7

[ 1 2 3 4 ] [ Some Matrix ] = [ 1 2 3 4 ] [ 1 2 3 4 ][ Some Matrix ]=[ 1 2 3 4 ]

• a. Find the “some matrix” that will make this matrix equation true.
• b. Test your answer by doing the multiplication to make sure it works out.

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

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

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?

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