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 #137 : Matrices

Perform the matrix operation $\begin{bmatrix} 4&2 &0 &1 \\ 3&2 &1 &7 \\ 3&4 &5 &1 \\ 2&3 &0 & 5 \end{bmatrix}+\begin{bmatrix} 4&2 &8 &0 \\ 5&3 &1 &6 \\ 5&11 &10 &2 \\ 4&6 &9 &1 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 1&4 &0 &0 \\ 15&3 &1 &42 \\ 15&44 &50 &2 \\ 7&18 &0 &1 \end{bmatrix}$

$\begin{bmatrix} 16&4 &0 &1 \\ 15&6 &1 &4 \\ 5&19 &50 &2 \\ 8&18 &0 &5 \end{bmatrix}$

$\begin{bmatrix} 1&4 &0 &0 \\ 15&6 &1 &4 \\ 15&44 &5 &2 \\ 8&8 &0 &5 \end{bmatrix}$

$\begin{bmatrix} 8&4 &8 &1 \\ 8&5 &2 &13 \\ 8&15 &15 &3 \\ 6&9 &9 &6 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 8&4 &8 &1 \\ 8&5 &2 &13 \\ 8&15 &15 &3 \\ 6&9 &9 &6 \end{bmatrix}$

Explanation:

To do matrix summation, you apply the following formula, where a and b are 4x4 matrices: $\begin{bmatrix} a&b &c &d \\ e&f &g &h \\ i&j &k &l \\ m&n & o&p \end{bmatrix}+\begin{bmatrix} q& r& s&t \\ u&v &w &x \\ y&z &a_1 &b_1 \\ c_1&d_1 &e_1 &f_1 \end{bmatrix}=\begin{bmatrix} a+q&b+r &c+s &d+t \\ e+u&f+v &g+w &h+x \\ i+y&j+z &k+a_{1} &l+b_{1} \\ m+c_{1}&n+d_{1} &o+e_{1} &p+f_{1} \end{bmatrix}$

Using this formula, we get $\begin{bmatrix} 8&4 &8 &1 \\ 8&5 &2 &13 \\ 8&15 &15 &3 \\ 6&9 &9 &6 \end{bmatrix}$

Report an Error

Example Question #731 : Vectors And Vector Operations

Find the determinant of the 3x3 matrix given: $\begin{bmatrix} 1&4 &7 \\ 3&7 &8 \\ 5&0 &6 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the the determinant of a 3x3 matrix $a=\begin{bmatrix} a& b&c \\ d&e &f \\ h&i &j \end{bmatrix}$ , you apply the following formula

determinant=a(ej-if)-b(dj-hf)+c(di-he)

Applying to the matrix from the problem statement, we get

1(42-0)-4(18-40)+7(0-35)=-115

Report an Error

Example Question #732 : Vectors And Vector Operations

Find the determinant of the 3x3 matrix given: $\begin{bmatrix} 2&0 &4 \\ 3&1 &6 \\ 5&2 &7 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the the determinant of a 3x3 matrix $a=\begin{bmatrix} a& b&c \\ d&e &f \\ h&i &j \end{bmatrix}$ , you apply the following formula

determinant=a(ej-if)-b(dj-hf)+c(di-he)

Applying to the matrix from the problem statement, we get

2(7-12)-0(21-30)+4(6-5)=-6

Report an Error

Example Question #732 : Vectors And Vector Operations

Find the determinant of the 2x2 matrix given: $\begin{bmatrix} 3&x \\ 7&2 \end{bmatrix}$

Possible Answers:

3x+9

6-7x

2x+3

6+7x

Correct answer:

6-7x

Explanation:

To find the determinant of a 2x2 matrix $a=\begin{bmatrix} x&y \\ z&q \end{bmatrix}$ , we use the formula:

detemrinant=xq-zy

Using the vector from the problem statement, we get:

(3*2)-(7*x)=6-7x

Report an Error

Example Question #141 : Matrices

Evaluate the matrix operation $\begin{bmatrix} 4&7 \\ 1&-3 \end{bmatrix}+\begin{bmatrix} 9&-4 \\ -2& -5 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 13&3 \\ -1&-8 \end{bmatrix}$

$\begin{bmatrix} 13&-3 \\ -1&-8 \end{bmatrix}$

$\begin{bmatrix} 15&3 \\ -1&-8 \end{bmatrix}$

$\begin{bmatrix} 13&3 \\ -1&-4 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 13&3 \\ -1&-8 \end{bmatrix}$

Explanation:

To find the sum of 2 2x2 matrices, we use the formula:

$\begin{bmatrix} a&b \\ c&d \end{bmatrix}+\begin{bmatrix} w&x \\ y& z \end{bmatrix}=\begin{bmatrix} a+w& b+x\\ c+y&d+z \end{bmatrix}$

Applying to the matrices from the problem statement, we get:

$\begin{bmatrix} 4+9&7-4 \\ 1-2&-3-5 \end{bmatrix}=\begin{bmatrix} 13&3 \\ -1&-8 \end{bmatrix}$

Report an Error

Example Question #733 : Vectors And Vector Operations

Find the determinant of the 2x2 matrix given: $\begin{bmatrix} 4&y \\ z&8 \end{bmatrix}$

Possible Answers:

32+yz

8y-4z

32-yz

4y-8z

Correct answer:

32-yz

Explanation:

To find the determinant of a 2x2 matrix $a=\begin{bmatrix} x&y \\ z&q \end{bmatrix}$ , we use the formula:

detemrinant=xq-zy

Using the vector from the problem statement, we get:

(4*8)-(y*z)=32-yz

Report an Error

Example Question #734 : Vectors And Vector Operations

Find the determinant of the matrix:

$\begin{vmatrix} 4&xy \\ x^2& y^2 \end{vmatrix}$

Possible Answers:

4y^2-x^3y

4y^2+x^3y

$\left \langle 4y^2, -x^3y \right \rangle$

Correct answer:

4y^2-x^3y

Explanation:

The determinant of a two-by-two matrix is given by

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

(The process is similar to the finding the cross product using a three-by-three matrix, where one moves from top left to bottom right, and then subtracts the result of moving from top right to bottom left).

Our final answer is 4y^2-x^3y .

Report an Error

Example Question #735 : Vectors And Vector Operations

Find the determinant of the 3x3 matrix $\begin{bmatrix} 1&5 &9 \\ 2& 1&0 \\ 6&3 &2 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 3x3 matrix $a=\begin{bmatrix} a&b &c \\ d& e&f \\ g& h&i \end{bmatrix}$ , we use the formula

determinant=a(ei-hf)-b(di-gf)+c(dh-ge)

Using the matrix from the problem statement, we get

determinant=1(2-0)-5(4-0)+9(6-6)=-18

Report an Error

Example Question #736 : Vectors And Vector Operations

Find the determinant of the 2x2 matrix $\begin{bmatrix} 4&2 \\ 8&3 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix $a=\begin{bmatrix} b& c\\ x&y \end{bmatrix}$ ,

we use the formula

determinant=by-xc

Using the matrix from the problem statement, we get

(4*3)-(8*2)=-4

Report an Error

Example Question #737 : Vectors And Vector Operations

Find the determinant of the 2x2 matrix $\begin{bmatrix} 5&-1\\ 12&3\end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To find the determinant of a 2x2 matrix $a=\begin{bmatrix} b& c\\ x&y \end{bmatrix}$ ,

we use the formula

determinant=by-xc

Using the matrix from the problem statement, we get

(5*3)-(12*-1)=27

Report an Error

View Calculus 3 Tutors

Dalton
Certified Tutor

University of Massachusetts Amherst, Doctor of Philosophy, Mathematics.

View Calculus 3 Tutors

Fathima
Certified Tutor

BITS Pilani Goa, Doctorate (PhD), Mathematics.

View Calculus 3 Tutors

Wysheka
Certified Tutor

Clemson University, Doctorate (PhD), Engineering and Science Education.

All Calculus 3 Resources

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

Popular Subjects

GMAT Tutors in Philadelphia, Chemistry Tutors in Seattle, Reading Tutors in New York City, Math Tutors in Seattle, Computer Science Tutors in Chicago, Reading Tutors in Denver, Statistics Tutors in Miami, MCAT Tutors in Philadelphia, Spanish Tutors in Seattle, SAT Tutors in San Diego

Popular Courses & Classes

SSAT Courses & Classes in Boston, SAT Courses & Classes in New York City, MCAT Courses & Classes in Boston, ACT Courses & Classes in Chicago, SSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Denver, Spanish Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Seattle, SSAT Courses & Classes in Miami, Spanish Courses & Classes in Atlanta

Popular Test Prep

MCAT Test Prep in Chicago, LSAT Test Prep in Phoenix, SSAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Washington DC, SSAT Test Prep in Denver, ACT Test Prep in New York City, ACT Test Prep in Chicago, ACT Test Prep in Denver, SSAT Test Prep in Seattle, SAT Test Prep in Los Angeles

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 #137 : Matrices

Example Question #731 : Vectors And Vector Operations

Example Question #732 : Vectors And Vector Operations

Example Question #732 : Vectors And Vector Operations

Example Question #141 : Matrices

Example Question #733 : Vectors And Vector Operations

Example Question #734 : Vectors And Vector Operations

Example Question #735 : Vectors And Vector Operations

Example Question #736 : Vectors And Vector Operations

Example Question #737 : Vectors And Vector Operations

All Calculus 3 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: