We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Linear Algebra : Norms

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 following vector.

A=[3,4,5]

Possible Answers:

$\left \| A\right \|=2\sqrt{5}$

$\left \| A\right \|=\sqrt{2}$

$\left \| A\right \|=5$

$\left \| A\right \|=5\sqrt{2}$

$\left \| A\right \|=\sqrt{52}$

Correct answer:

$\left \| A\right \|=5\sqrt{2}$

Explanation:

The norm of a vector is simply the square root of the sum of each component squared.

$\left \| A\right \|=\sqrt{3^2+4^2+5^2}=\sqrt{9+16+25}=\sqrt{50}=5\sqrt{2}$

Report an Error

Example Question #1 : Norms

Find the norm of vector .

$A=(\cos(x), \sin(x))$

Possible Answers:

$\left \| A\right \|=1+\sin^2(x)$

$\left \| A\right \|=0$

$\left \| A\right \|=1$

$\left \| A\right \|=1+\cos^2(x)$

$\left \| A\right \|=\cos(x)+\sin(x)$

Correct answer:

$\left \| A\right \|=1$

Explanation:

In order to find the norm, we need to square each component, sum them up, and then take the square root.

$\left \| A\right \|=\sqrt{\cos^2(x)+\sin^2(x)}=\sqrt{1}=1$

Report an Error

Example Question #1 : Norms

Find the norm, $\begin{Vmatrix} \bf{a} \end{Vmatrix}$ , given $\bf{a}= \begin{bmatrix} 2\\ 1\\ 7\\ -2 \end{bmatrix}$

Possible Answers:

$\begin{Vmatrix} \bf{a} \end{Vmatrix}=\sqrt{8}$

$\begin{Vmatrix} \bf{a} \end{Vmatrix}=\sqrt{58}$

$\begin{Vmatrix} \bf{a} \end{Vmatrix}=58$

$\begin{Vmatrix} \bf{a} \end{Vmatrix}=-28$

Correct answer:

$\begin{Vmatrix} \bf{a} \end{Vmatrix}=\sqrt{58}$

Explanation:

By definition,

$\begin{Vmatrix} \bf{a} \end{Vmatrix}= \sqrt{a_1^2+a_2^2+a_3^2+...+a_n^2}$ ,

therefore,

$\begin{Vmatrix} \bf{a} \end{Vmatrix}= \sqrt{2^2+1^2+7^2+(-2)^2}= \sqrt{58}$ .

Report an Error

Example Question #1 : Norms

Calculate the norm of $\bf{A}\times \bf{B}$ , or $\begin{Vmatrix} \bf{A}\times \bf{B} \end{Vmatrix}$ , given

$\bf{A} = 3 \hat{i} - 1 \hat{j}$ ,

$\bf{B} = -1 \hat{k}$ .

Possible Answers:

Can not be determined.

$\begin{Vmatrix} \bf{A}\times \bf{B} \end{Vmatrix}= 10$

$\begin{Vmatrix} \bf{A}\times \bf{B} \end{Vmatrix}= 4$

$\begin{Vmatrix} \bf{A}\times \bf{B} \end{Vmatrix}=\sqrt{10}$

Correct answer:

$\begin{Vmatrix} \bf{A}\times \bf{B} \end{Vmatrix}=\sqrt{10}$

Explanation:

First, we need to find $\bf{A}\times \bf{B}$ . This is, by definition,

$\bf{A \times \bf{B}}= \begin{vmatrix} \hat{i}&\hat{j} &\hat{k} \\ 3& -1& 0\\ 0&0 &-1 \end{vmatrix}= 1\hat{i}+3\hat{j}$ .

Therefore,

$\begin{Vmatrix} \bf{A}\times \bf{B} \end{Vmatrix}=\sqrt{1^2+3^2}=\sqrt{10}$ .

Report an Error

Example Question #1 : Norms

Find the norm of the vector $\vec{v} = (4, 3, 0)$

Possible Answers:

$\sqrt{7}$

Correct answer:

Explanation:

To find the norm, square each component, add, then take the square root:

$\sqrt{4^2 + 3^2 + 0^2 } = \sqrt{16 + 9 } = \sqrt{25 } = 5$

Report an Error

Example Question #1 : Norms

Find a unit vector in the same direction as $\vec{v} = (2, -3, \sqrt{3})$

Possible Answers:

(4,4,4)

$(\frac{2}{\sqrt{2}}, -\frac{3}{\sqrt{2}}, \sqrt{\frac{3}{2}})$

$(\frac{1}{2} , -\frac{3}{4} , \frac{\sqrt{3}}{4})$

$(1, -1.5, \frac{\sqrt3}{2} )$

Correct answer:

$(\frac{1}{2} , -\frac{3}{4} , \frac{\sqrt{3}}{4})$

Explanation:

First, find the length of the vector: $\sqrt{ 2^2 + (-3)^2 + (\sqrt{3})^2 } = \sqrt{4+9+3} = \sqrt{16} = 4$

Because this vector has the length of 4 and a unit vector would have a length of 1, divide everything by 4:

$( \frac{ 2}{4} , \frac{-3}{4} , \frac{\sqrt{3}}{4}) = (\frac{1}{2} , -\frac{3}{4} , \frac{\sqrt{3}}{4})$

Report an Error

Example Question #1 : Norms

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

Possible Answers:

$\sqrt{6}$

$2 \sqrt{3}$

$3 \sqrt{2}$

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:

$\sqrt{14 }$

$\sqrt{10}$

$\sqrt{4}$

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:

$3 \sqrt{5}$

$5 \sqrt{2}$

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

View Linear Algebra Tutors

Balamurugan
Certified Tutor

University of Delaware, Bachelor of Engineering, Chemical Engineering.

View Linear Algebra Tutors

Reza
Certified Tutor

University of Sherbrooke, Doctor of Philosophy, Mathematics. University of Manitoba, Master of Science, Mathematics.

View Linear Algebra Tutors

Eric
Certified Tutor

Georgia Highlands College, Associate in Science, Computer Science. Kennesaw State University, Bachelor of Science, Computer E...

All Linear Algebra Resources

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

Popular Subjects

French Tutors in Washington DC, Computer Science Tutors in San Francisco-Bay Area, Computer Science Tutors in New York City, Calculus Tutors in San Francisco-Bay Area, MCAT Tutors in Miami, ACT Tutors in Phoenix, Algebra Tutors in Boston, Chemistry Tutors in Chicago, Reading Tutors in Phoenix, Computer Science Tutors in Seattle

Popular Courses & Classes

Spanish Courses & Classes in Boston, LSAT Courses & Classes in Atlanta, ACT Courses & Classes in Chicago, SSAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Boston, ISEE Courses & Classes in Philadelphia, LSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Chicago, SSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Denver

Popular Test Prep

ISEE Test Prep in Atlanta, SSAT Test Prep in Houston, GMAT Test Prep in Houston, SAT Test Prep in Atlanta, GRE Test Prep in Boston, GRE Test Prep in Washington DC, MCAT Test Prep in New York City, ACT Test Prep in Chicago, ISEE Test Prep in Denver, GRE Test Prep in San Diego

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 : Norms

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 #1 : Norms

Example Question #1 : Norms

Example Question #1 : Norms

Example Question #1 : Norms

Example Question #1 : Norms

Example Question #1 : Norms

All Linear Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: