We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 3 : Matrices

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 #1 : Matrices

Calculate the determinant of Matrix .

$A=\begin{bmatrix} 1 & 2&3 \\ 0& 2& 1\\ 3& 4& 5 \end{bmatrix}$

Possible Answers:

$\det(A)=0$

$\det(A)=1$

$\det(A)=6$

$\det(A)=-2$

$\det(A)=-6$

Correct answer:

$\det(A)=-6$

Explanation:

In order to find the determinant of , we first need to copy down the first two columns into columns 4 and 5.

$A=\begin{bmatrix} 1 & 2&3 & 1 &2\\ 0& 2& 1&0 &2\\ 3& 4& 5 &3 &4\end{bmatrix}$

The next step is to multiply the down diagonals.

$A_d=1\cdot2\cdot5+2\cdot1\cdot 3+3\cdot0\cdot4=10+6+0=16$

The next step is to multiply the up diagonals.

$A_u=3\cdot2\cdot3+4\cdot1\cdot1+5\cdot0\cdot2=18+4=22$

The last step is to substract A_u from A_d .

$\det(A)=A_d-A_u=16-22=-6$

Report an Error

Example Question #1 : Matrices

Calculate the determinant of Matrix .

$A=\begin{bmatrix} 0 & 1&5 \\ 10& -3& 2\\ 1& 2& -5 \end{bmatrix}$

Possible Answers:

$\det(A)=-38$

$\det(A)=0$

$\det(A)=67$

$\det(A)=38$

$\det(A)=167$

Correct answer:

$\det(A)=167$

Explanation:

In order to find the determinant of , we first need to copy down the first two columns into columns 4 and 5.

$A=\begin{bmatrix} 0 & 1&5 & 0 &1\\ 10& -3& 2&10 &-3\\ 1& 2& -5 &1 &2\end{bmatrix}$

The next step is to multiply the down diagonals.

$A_d=0\cdot-3\cdot-5+1\cdot2\cdot 1+5\cdot10\cdot2=0+2+100=102$

The next step is to multiply the up diagonals.

$A_u=1\cdot-3\cdot5+2\cdot2\cdot0+(-5)\cdot10\cdot1=-15+0-50=-65$

The last step is to substract A_u from A_d .

$\det(A)=A_d-A_u=102-(-65)=167$

Report an Error

Example Question #1 : Matrices

Calculate the determinant of .

$A=\begin{bmatrix} 3 & 4\\ -2 & 10 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

All we need to do is multiply the main diagonal and substract it from the off diagonal.

$\det(A)=3\cdot10-4(-2)=30+8=38$

Report an Error

Example Question #1 : Matrices

Which of the following is a way to represent the computation $<2,6,1> \cdot <5,2,4>$ using matrices?

Possible Answers:

$\begin{bmatrix} 2 & 6 & 1 \end{bmatrix} \begin{bmatrix} 5& 2 & 4 \end{bmatrix}$

All of the above answers

$\begin{bmatrix} 2 & 6 & 1 \end{bmatrix} \begin{bmatrix} 5\\ 2\\ 4\\ \end{bmatrix}$

None of the other answers

$\begin{bmatrix} 2 \\ 6 \\ 1 \end{bmatrix} \begin{bmatrix} 5 \\ 2 \\ 4 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 2 & 6 & 1 \end{bmatrix} \begin{bmatrix} 5\\ 2\\ 4\\ \end{bmatrix}$

Explanation:

This choice is the only pair with a well-defined operation; the others are meaningless in terms of matrix multiplication.

Computing this we get

$\begin{bmatrix} 2 & 6 & 1 \end{bmatrix} \begin{bmatrix} 5\\ 2\\ 4\\ \end{bmatrix} = (2)(5)+(6)(2)+(1)(4) =26$ .

Which is the same as

$<2,6,1> \cdot <5,2,4> = (2)(5)+(6)(2)+(1)(4) =26$ .

This operation is true for (real) -dimensional vectors in general;

$\begin{bmatrix} a & b & c \end{bmatrix} \begin{bmatrix} d\\ e\\ f\\ \end{bmatrix} = ad+be+cf$

Report an Error

Example Question #2 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 1&2 \\ 5& 9\end{vmatrix}$

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 $A=\begin{vmatrix} 1&2 \\ 5& 9\end{vmatrix}$

The determinant is thus:

|A|=9-10=-1

Report an Error

Example Question #1 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 4&2 \\-1 &3 \end{vmatrix}$

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 $A=\begin{vmatrix} 4&2 \\-1 &3 \end{vmatrix}$

The determinant is thus:

|A|=12-(-2)=14

Report an Error

Example Question #7 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 5& 2\\ 3&1 \end{vmatrix}$

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 $A=\begin{vmatrix} 5& 2\\ 3&1 \end{vmatrix}$

The determinant is thus:

|A|=5-6=-1

Report an Error

Example Question #8 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 4&4 \\4 &2 \end{vmatrix}$

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 $A=\begin{vmatrix} 4&4 \\4 &2 \end{vmatrix}$

The determinant is thus:

|A|=8-16=-8

Report an Error

Example Question #1 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 9&3 \\21 &11 \end{vmatrix}$

Possible Answers:

249

162

156

213

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 $A=\begin{vmatrix} 9&3 \\21 &11 \end{vmatrix}$

The determinant is thus:

|A|=99-63=36

Report an Error

Example Question #10 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 11&3 \\2 &4 \end{vmatrix}$

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 $A=\begin{vmatrix} 11&3 \\2 &4 \end{vmatrix}$

The determinant is thus:

|A|=44-6=38

Report an Error

View Calculus 3 Tutors

Eugene
Certified Tutor

San Jacinto Community College, Associate in Arts, Mathematics. University of Houston, Bachelor of Science, Mechanical Enginee...

View Calculus 3 Tutors

Pankaj
Certified Tutor

University of Delhi, Electrical Engineer, Electrical Engineering. Columbia University in the City of New York, Master of Arts...

View Calculus 3 Tutors

Cole
Certified Tutor

Louisiana State University-Alexandria, Bachelor of Science, Computer Engineering, General. Louisiana State University-Alexand...

All Calculus 3 Resources

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

Popular Subjects

ACT Tutors in Los Angeles, GMAT Tutors in Los Angeles, Computer Science Tutors in Los Angeles, Algebra Tutors in Chicago, MCAT Tutors in San Diego, SSAT Tutors in Philadelphia, Statistics Tutors in Phoenix, Physics Tutors in Denver, Physics Tutors in San Francisco-Bay Area, Physics Tutors in Atlanta

Popular Courses & Classes

ACT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Boston, MCAT Courses & Classes in Boston, LSAT Courses & Classes in Phoenix, MCAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Los Angeles, ACT Courses & Classes in Philadelphia, SSAT Courses & Classes in Philadelphia, ACT Courses & Classes in San Diego, ISEE Courses & Classes in Miami

Popular Test Prep

ISEE Test Prep in New York City, GMAT Test Prep in Houston, ISEE Test Prep in Los Angeles, ACT Test Prep in San Francisco-Bay Area, SAT Test Prep in Atlanta, MCAT Test Prep in Miami, GRE Test Prep in Seattle, ACT Test Prep in San Diego, SSAT Test Prep in Atlanta, GMAT Test Prep in Seattle

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 : Matrices

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #1 : Matrices

Example Question #1 : Matrices

Example Question #1 : Matrices

Example Question #1 : Matrices

Example Question #2 : Matrices

Example Question #1 : Matrices

Example Question #7 : Matrices

Example Question #8 : Matrices

Example Question #1 : Matrices

Example Question #10 : Matrices

All Calculus 3 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: