<< Chapter < Page Chapter >> Page >

Section exercises

Verbal

Explain why we can always evaluate the determinant of a square matrix.

A determinant is the sum and products of the entries in the matrix, so you can always evaluate that product—even if it does end up being 0.

Got questions? Get instant answers now!

Examining Cramer’s Rule, explain why there is no unique solution to the system when the determinant of your matrix is 0. For simplicity, use a 2 × 2 matrix.

Got questions? Get instant answers now!

Explain what it means in terms of an inverse for a matrix to have a 0 determinant.

The inverse does not exist.

Got questions? Get instant answers now!

The determinant of 2 × 2 matrix A is 3. If you switch the rows and multiply the first row by 6 and the second row by 2, explain how to find the determinant and provide the answer.

Got questions? Get instant answers now!

Algebraic

For the following exercises, find the determinant.

| 2 3 3.1 4 , 000 |

7 , 990.7

Got questions? Get instant answers now!

| 1.1 0.6 7.2 0.5 |

Got questions? Get instant answers now!

| 1 0 0 0 1 0 0 0 3 |

3

Got questions? Get instant answers now!

| 1 4 0 0 2 3 0 0 3 |

Got questions? Get instant answers now!

| 1 0 1 0 1 0 1 0 0 |

1

Got questions? Get instant answers now!

| 2 3 1 3 4 1 5 6 1 |

Got questions? Get instant answers now!

| 2 1 4 4 2 8 2 8 3 |

224

Got questions? Get instant answers now!

| 6 1 2 4 3 5 1 9 1 |

Got questions? Get instant answers now!

| 5 1 1 2 3 1 3 6 3 |

15

Got questions? Get instant answers now!

| 1.1 2 1 4 0 0 4.1 0.4 2.5 |

Got questions? Get instant answers now!

| 2 1.6 3.1 1.1 3 8 9.3 0 2 |

17.03

Got questions? Get instant answers now!

| 1 2 1 3 1 4 1 5 1 6 1 7 0 0 1 8 |

Got questions? Get instant answers now!

For the following exercises, solve the system of linear equations using Cramer’s Rule.

2 x 3 y = −1 4 x + 5 y = 9

( 1 , 1 )

Got questions? Get instant answers now!

5 x 4 y = 2 4 x + 7 y = 6

Got questions? Get instant answers now!

   6 x 3 y = 2 8 x + 9 y = −1

( 1 2 , 1 3 )

Got questions? Get instant answers now!

2 x + 6 y = 12 5 x 2 y = 13

Got questions? Get instant answers now!

4 x + 3 y = 23    2 x y = −1

( 2 , 5 )

Got questions? Get instant answers now!

10 x 6 y = 2 5 x + 8 y = −1

Got questions? Get instant answers now!

4 x 3 y = −3 2 x + 6 y = −4

( 1 , 1 3 )

Got questions? Get instant answers now!

4 x 5 y = 7 3 x + 9 y = 0

Got questions? Get instant answers now!

4 x + 10 y = 180 3 x 5 y = −105

( 15 , 12 )

Got questions? Get instant answers now!

   8 x 2 y = −3 4 x + 6 y = 4

Got questions? Get instant answers now!

For the following exercises, solve the system of linear equations using Cramer’s Rule.

     x + 2 y 4 z = 1    7 x + 3 y + 5 z = 26 2 x 6 y + 7 z = 6

( 1 , 3 , 2 )

Got questions? Get instant answers now!

5 x + 2 y 4 z = 47      4 x 3 y z = 94     3 x 3 y + 2 z = 94

Got questions? Get instant answers now!

     4 x + 5 y z = −7 −2 x 9 y + 2 z = 8            5 y + 7 z = 21

( 1 , 0 , 3 )

Got questions? Get instant answers now!

4 x 3 y + 4 z = 10 5 x 2 z = 2 3 x + 2 y 5 z = 9

Got questions? Get instant answers now!

4 x 2 y + 3 z = 6       6 x + y = 2 2 x + 7 y + 8 z = 24

( 1 2 , 1 , 2 )

Got questions? Get instant answers now!

5 x + 2 y z = 1 7 x 8 y + 3 z = 1.5 6 x 12 y + z = 7

Got questions? Get instant answers now!

   13 x 17 y + 16 z = 73 11 x + 15 y + 17 z = 61    46 x + 10 y 30 z = 18

( 2 , 1 , 4 )

Got questions? Get instant answers now!

4 x 3 y 8 z = 7    2 x 9 y + 5 z = 0.5    5 x 6 y 5 z = 2

Got questions? Get instant answers now!

   4 x 6 y + 8 z = 10 2 x + 3 y 4 z = 5           x + y + z = 1

Infinite solutions

Got questions? Get instant answers now!

4 x 6 y + 8 z = 10 2 x + 3 y 4 z = 5 12 x + 18 y 24 z = 30

Got questions? Get instant answers now!

Technology

For the following exercises, use the determinant function on a graphing utility.

| 1 0 8 9 0 2 1 0 1 0 3 0 0 2 4 3 |

24

Got questions? Get instant answers now!

| 1 0 2 1 0 −9 1 3 3 0 −2 −1 0 1 1 −2 |

Got questions? Get instant answers now!

| 1 2 1 7 4 0 1 2 100 5 0 0 2 2,000 0 0 0 2 |

1

Got questions? Get instant answers now!

| 1 0 0 0 2 3 0 0 4 5 6 0 7 8 9 0 |

Got questions? Get instant answers now!

Real-world applications

For the following exercises, create a system of linear equations to describe the behavior. Then, calculate the determinant. Will there be a unique solution? If so, find the unique solution.

Two numbers add up to 56. One number is 20 less than the other.

Yes; 18, 38

Got questions? Get instant answers now!

Two numbers add up to 104. If you add two times the first number plus two times the second number, your total is 208

Got questions? Get instant answers now!

Three numbers add up to 106. The first number is 3 less than the second number. The third number is 4 more than the first number.

Yes; 33, 36, 37

Got questions? Get instant answers now!

Three numbers add to 216. The sum of the first two numbers is 112. The third number is 8 less than the first two numbers combined.

Got questions? Get instant answers now!

For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.

You invest $10,000 into two accounts, which receive 8% interest and 5% interest. At the end of a year, you had $10,710 in your combined accounts. How much was invested in each account?

$7,000 in first account, $3,000 in second account.

Got questions? Get instant answers now!

Questions & Answers

the diagram of the digestive system
Assiatu Reply
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
Aron Reply
Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
Allison Reply
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 2

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask