Call Now to Set Up Tutoring:

(888) 888-0446

Linear Algebra : Operations and Properties

Study concepts, example questions & explanations for Linear Algebra

Create An Account

All Linear Algebra Resources

4 Diagnostic Tests 108 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Norms

Find the norm of the vector $\vec{v} = (-1, 3, 2,2)$

Possible Answers:

$3 \sqrt{2}$

$2 \sqrt{3}$

$\sqrt{6}$

Correct answer:

$3 \sqrt{2}$

Explanation:

$|| \vec{v} || = \sqrt{ (-1)^2 + 3^2 + 2^2 + 2^2 } = \sqrt{ 1 + 9 + 4 + 4 } = \sqrt{18}$

This can be simplified:

$\sqrt{18 } = \sqrt{3\cdot3\cdot2 } = 3 \sqrt{2 }$

Report an Error

Example Question #1 : Norms

Find the norm of the vector $\vec{v} = (2, -3, 1 )$

Possible Answers:

$\sqrt{4}$

$\sqrt{14 }$

$\sqrt{10}$

Correct answer:

$\sqrt{14 }$

Explanation:

$|| \vec{v} || = \sqrt{2^2 + (-3)^2 + 1^2 } = \sqrt{4+9+1} = \sqrt{14}$

Report an Error

Example Question #1 : Norms

Find the norm of the vector $\vec{v}= (4, 2, -5 )$

Possible Answers:

$5 \sqrt{2}$

$3 \sqrt{5}$

Correct answer:

$3 \sqrt{5}$

Explanation:

$|| \vec{v} || = \sqrt{ 4^2 + 2^2 + (-5)^2 } = \sqrt{16 + 4 + 25 } = \sqrt{45}$

This can be simplified:

$\sqrt{3 \cdot 3 \cdot 5 } = 3 \sqrt {5}$

Report an Error

Example Question #1 : Norms

Find the norm of the vector $\vec{v} = (2, -3, -6 )$

Possible Answers:

$\sqrt{23}$

$\sqrt{41 }$

Correct answer:

Explanation:

$|| \vec{v} || = \sqrt{ 2^2 + (-3)^2 + (-6)^2 } = \sqrt{4 + 9 + 36 } = \sqrt{49} = 7$

Report an Error

Example Question #141 : Operations And Properties

Find the norm of the vector $\vec{v} = (3, -2, -2)$

Possible Answers:

$\sqrt{17}$

$\sqrt{7}$

$\sqrt{15}$

Correct answer:

$\sqrt{17}$

Explanation:

$|| \vec{v} || = \sqrt{3^2 + (-2)^2 + (-2)^2 } = \sqrt{9+4+4} = \sqrt{17}$

Report an Error

Example Question #142 : Operations And Properties

Find the norm of the vector $\vec{v} = (4, -1, 3 )$

Possible Answers:

$\sqrt{6}$

$\sqrt{26}$

$\sqrt{24}$

Correct answer:

$\sqrt{26}$

Explanation:

$|| \vec{v} || = \sqrt{ 4^2 + (-1)^2 + 3^2 } = \sqrt{16+1+9 } = \sqrt{26}$

Report an Error

Example Question #143 : Operations And Properties

Find the norm of the vector $\vec{v} = (3, 4, 5 )$

Possible Answers:

$5 \sqrt{2}$

$2 \sqrt{3}$

$3 \sqrt{2}$

$2\sqrt{5}$

Correct answer:

$5 \sqrt{2}$

Explanation:

$|| \vec{v} || = \sqrt{ 3^2 + 4^2 + 5^2 } = \sqrt{9+16+25} = \sqrt{50 }$

This can be simplified:

$\sqrt{2 \cdot 5 \cdot 5 } = 5 \sqrt{2 }$

Report an Error

Example Question #11 : Norms

Let $\textbf{u} = (2, 3, a, 1 )$ for some real number .

Give such that $\left \| \textbf{u} \right \| = 4$ .

Possible Answers:

$\pm \frac{16}{13}$

$\pm \sqrt{2}$

$\pm \frac{4 \sqrt{13}}{13}$

$\frac{2}{3}$

Correct answer:

$\pm \sqrt{2}$

Explanation:

$\left \| \textbf{u} \right \|$ , the norm, or length, of vector $\textbf{u}$ , is equal to the square root of the sum of the squares of its elements. Therefore,

$\left \| \textbf{u} \right \| = \sqrt{2^{2}+3^{2}+a^{2}+1^{2}}$

$= \sqrt{4+9+a^{2}+1}$

$= \sqrt{ a^{2}+14}$

Set this equal to 4:

$\sqrt{ a^{2}+14} = 4$

$a^{2}+14 = 16$

$a^{2}= 2$

$a = \pm \sqrt{2}$

Report an Error

Example Question #144 : Operations And Properties

$\textbf{u}= (-3, 2, x, x)$ ,

where is a real number.

In terms of , give $\left \| \textbf{u} \right \|$ .

Possible Answers:

$\sqrt{2x-1}$

$\sqrt{2 x ^{2} +13}$

$x \sqrt{6}$

$\sqrt{2x+5}$

$\sqrt{2 x ^{2} -5}$

Correct answer:

$\sqrt{2 x ^{2} +13}$

Explanation:

$\left \| \textbf{u} \right \|$ , the norm, or length, of vector $\textbf{u}$ , is equal to the square root of the sum of the squares of its elements. Therefore,

$\left \| \textbf{u} \right \|= \sqrt{(-3)^{2}+ 2 ^{2}+ x ^{2} +x ^{2}}$

$=\sqrt{9+4+ x ^{2} +x ^{2}}$

$=\sqrt{2 x ^{2} +13}$

Report an Error

Example Question #223 : Linear Algebra

$\bold{v} = \left ( \frac{1}{3}, - \frac{1}{3},\frac{1}{3} \right )$

True or false: $\textbf{v}$ is an example of a unit vector.

Possible Answers:

False

True

Correct answer:

False

Explanation:

$\textbf{v}$ is a unit vector if and only if its norm, or length, $\left \| \textbf{v} \right \|$ - the square root of the sum of the squares of its elements - is equal to 1. Find the length using this definition:

$\left \| \textbf{v} \right \| = \sqrt{\left ( \frac{1}{3} \right )^{2}+ \left ( -\frac{1}{3} \right )^{2}+ \left ( \frac{1}{3} \right )^{2}}$

$= \sqrt{\frac{1}{9}+ \frac{1}{9} + \frac{1}{9} }$

$= \sqrt{\frac{1}{3} }$

$\left \| \textbf{v} \right \| \ne 1$ , so $\textbf{v}$ is not a unit vector.

Report an Error

View Linear Algebra Tutors

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

View Linear Algebra Tutors

Ali
Certified Tutor

university of Trieste, Bachelor of Science, Industrial Engineering. University of Huelva, Master of Science, Aircraft Armamen...

View Linear Algebra Tutors

Ping
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science. University of North Texas, Master of Arts, Education.

All Linear Algebra Resources

4 Diagnostic Tests 108 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Chicago, ISEE Tutors in San Diego, English Tutors in Boston, Physics Tutors in Houston, Computer Science Tutors in Denver, Algebra Tutors in Miami, SAT Tutors in Washington DC, SSAT Tutors in Houston, SAT Tutors in Phoenix, Algebra Tutors in New York City

Popular Courses & Classes

GMAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in San Diego, ISEE Courses & Classes in Phoenix, ACT Courses & Classes in Denver, SSAT Courses & Classes in Seattle, SAT Courses & Classes in San Diego, GMAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Atlanta, GRE Courses & Classes in Washington DC, SSAT Courses & Classes in Washington DC

Popular Test Prep

SSAT Test Prep in New York City, GRE Test Prep in San Diego, GRE Test Prep in Boston, GMAT Test Prep in Philadelphia, SSAT Test Prep in Seattle, GMAT Test Prep in San Diego, GMAT Test Prep in San Francisco-Bay Area, ACT Test Prep in New York City, MCAT Test Prep in Seattle, SAT Test Prep in Washington DC

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Linear Algebra : Operations and Properties

Study concepts, example questions & explanations for Linear Algebra

All Linear Algebra Resources

Example Questions

Example Question #1 : Norms

Example Question #1 : Norms

Example Question #1 : Norms

Example Question #1 : Norms

Example Question #141 : Operations And Properties

Example Question #142 : Operations And Properties

Example Question #143 : Operations And Properties

Example Question #11 : Norms

Example Question #144 : Operations And Properties

Example Question #223 : Linear Algebra

All Linear Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: