We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 3 : Vectors and Vector Operations

Study concepts, example questions & explanations for Calculus 3

Create An Account

All Calculus 3 Resources

6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #661 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 5&16 \\8 &16 \end{vmatrix}$

Possible Answers:

231

208

281

307

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 5&16 \\8 &16 \end{vmatrix}$

The determinant is thus:

|A|=80-128=-48

Report an Error

Example Question #61 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 4& 11\\17 & 22\end{vmatrix}$

Possible Answers:

129

275

174

310

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 4& 11\\17 & 22\end{vmatrix}$

The determinant is thus:

|A|=88-187=-99

Report an Error

Example Question #662 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 12& 17\\6 & 4\end{vmatrix}$

Possible Answers:

140

150

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 12& 17\\6 & 4\end{vmatrix}$

The determinant is thus:

|A|=48-102=-54

Report an Error

Example Question #663 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 14&5 \\-1 &8 \end{vmatrix}$

Possible Answers:

117

107

112

Correct answer:

117

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 14&5 \\-1 &8 \end{vmatrix}$

The determinant is thus:

|A|=112-(-5)=117

Report an Error

Example Question #71 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -1& 0\\11 &5 \end{vmatrix}$

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} -1& 0\\11 &5 \end{vmatrix}$

The determinant is thus:

|A|=-5-0=-5

Report an Error

Example Question #72 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 14& 12\\-14 &-14 \end{vmatrix}$

Possible Answers:

364

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} 14& 12\\-14 &-14 \end{vmatrix}$

The determinant is thus:

|A|=-196-(-168)=-28

Report an Error

Example Question #73 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -5&-13 \\6 &5 \end{vmatrix}$

Possible Answers:

Correct answer:

Explanation:

The determinant of a 2x2 matrix can be found by cross multiplying terms as follows:

$det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc$

For the matrix $A=\begin{vmatrix} -5&-13 \\6 &5 \end{vmatrix}$

The determinant is thus:

|A|=-25-(-78)=53

Report an Error

Example Question #74 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -12&8 &3 \\15 &15 & -7\\-10 &-1 &-12 \end{vmatrix}$

Possible Answers:

4649

2315

4721

Correct answer:

4649

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

$det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a\begin{Vmatrix} e&f \\ h&i \end{Vmatrix}-b\begin{Vmatrix} d&f \\ g&i \end{Vmatrix}+c\begin{Vmatrix} d&e \\ g&h \end{Vmatrix}$

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

$det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$

For the matrix $A=\begin{vmatrix} -12&8 &3 \\15 &15 & -7\\-10 &-1 &-12 \end{vmatrix}$

The determinant is thus:

{|A|=-12[15(-12)-(-1)(-7)]-8[15(-12)-(-10)(-7)]+3[15(-1)-(-10)(15)]=4649}

Report an Error

Example Question #75 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix}10 &2 &-10 \\14 &-13 &2 \\-11 & 10& 2\end{vmatrix}$

Possible Answers:

1080

540

Correct answer:

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

$det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a\begin{Vmatrix} e&f \\ h&i \end{Vmatrix}-b\begin{Vmatrix} d&f \\ g&i \end{Vmatrix}+c\begin{Vmatrix} d&e \\ g&h \end{Vmatrix}$

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

$det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$

For the matrix $A=\begin{vmatrix}10 &2 &-10 \\14 &-13 &2 \\-11 & 10& 2\end{vmatrix}$

The determinant is thus:

{|A|=10[-13(2)-10(2)]-2[14(2)-(-11)(2)]+(-10)[14(10)-(-11)(-13)]=-530}

Report an Error

Example Question #76 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 14&10 &-4 \\-7 &10 &-11 \\14 &4 &2 \end{vmatrix}$

Possible Answers:

168

396

742

Correct answer:

168

Explanation:

The determinant of a 3x3 matrix can be found via a means of reduction into three 2x2 matrices as follows:

$det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a\begin{Vmatrix} e&f \\ h&i \end{Vmatrix}-b\begin{Vmatrix} d&f \\ g&i \end{Vmatrix}+c\begin{Vmatrix} d&e \\ g&h \end{Vmatrix}$

These can then be further reduced via the method of finding the determinant of a 2x2 matrix:

$det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$

For the matrix $A=\begin{vmatrix} 14&10 &-4 \\-7 &10 &-11 \\14 &4 &2 \end{vmatrix}$

The determinant is thus:

{|A|=14[10(2)-4(-11)]-10[-7(2)-14(-11)]+(-4)[-7(4)-14(10)]=168}

Report an Error

View Calculus 3 Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Calculus 3 Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Calculus 3 Tutors

Kurosh
Certified Tutor

University of tehran, Bachelor of Engineering, Electrical Engineering.

All Calculus 3 Resources

6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Los Angeles, MCAT Tutors in Atlanta, MCAT Tutors in Chicago, SSAT Tutors in Chicago, ACT Tutors in Atlanta, Calculus Tutors in Denver, Spanish Tutors in Denver, Reading Tutors in San Francisco-Bay Area, Chemistry Tutors in Houston, Physics Tutors in San Diego

Popular Courses & Classes

LSAT Courses & Classes in Chicago, LSAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in New York City, ACT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Atlanta, SAT Courses & Classes in Miami, SAT Courses & Classes in Atlanta, MCAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Miami

Popular Test Prep

MCAT Test Prep in San Diego, GMAT Test Prep in San Diego, LSAT Test Prep in San Diego, GRE Test Prep in Phoenix, ACT Test Prep in San Francisco-Bay Area, ACT Test Prep in Dallas Fort Worth, LSAT Test Prep in Denver, SSAT Test Prep in Los Angeles, ISEE Test Prep in Los Angeles, SAT Test Prep in Philadelphia

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

Calculus 3 : Vectors and Vector Operations

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #661 : Vectors And Vector Operations

Example Question #61 : Matrices

Example Question #662 : Vectors And Vector Operations

Example Question #663 : Vectors And Vector Operations

Example Question #71 : Matrices

Example Question #72 : Matrices

Example Question #73 : Matrices

Example Question #74 : Matrices

Example Question #75 : Matrices

Example Question #76 : Matrices

All Calculus 3 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: