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 #91 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 15& -15& -15\\10 &-13 &-9 \\11 &3 &-1 \end{vmatrix}$

Possible Answers:

1354

880

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 $A=\begin{vmatrix} 15& -15& -15\\10 &-13 &-9 \\11 &3 &-1 \end{vmatrix}$

The determinant is thus:

{|A|=15[-13(-1)-3(-9)]-(-15)[10(-1)-11(-9)]+(-15)[10(3)-11(-13)]=-660}

Report an Error

Example Question #92 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 5& 0&-5 \\-7 &8 &-6 \\ -2&-9 &4 \end{vmatrix}$

Possible Answers:

271

809

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 $A=\begin{vmatrix} 5& 0&-5 \\-7 &8 &-6 \\ -2&-9 &4 \end{vmatrix}$

The determinant is thus:

{|A|=5[8(4)-(-9)(-6)]-0[-7(4)-(-2)(-6)]+(-5)[-7(-9)-(-2)(8)]=-505}

Report an Error

Example Question #2681 : Calculus 3

Find the determinant of the matrix $A=\begin{vmatrix}-6 &-9 &-5 \\-1 &8 &6 \\-3 &6 & 7\end{vmatrix}$

Possible Answers:

444

384

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 $A=\begin{vmatrix}-6 &-9 &-5 \\-1 &8 &6 \\-3 &6 & 7\end{vmatrix}$

The determinant is thus:

{|A|=-6[8(7)-6(6)]-(-9)[-1(7)-(-3)(6)]+(-5)[-1(6)-(-3)(8)]=-111}

Report an Error

Example Question #682 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 9&8 &-5 \\2 &-5 &7 \\8 &9 &8 \end{vmatrix}$

Possible Answers:

903

1544

477

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 $A=\begin{vmatrix} 9&8 &-5 \\2 &-5 &7 \\8 &9 &8 \end{vmatrix}$

The determinant is thus:

|A|=9[-5(8)-9(7)]-8[2(8)-8(7)]+(-5)[2(9)-8(-5)]=-897

Report an Error

Example Question #95 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} 2& -6&8 \\4 &-4 &2 \\8 &0 & -5\end{vmatrix}$

Possible Answers:

311

405

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 $A=\begin{vmatrix} 2& -6&8 \\4 &-4 &2 \\8 &0 & -5\end{vmatrix}$

The determinant is thus:

|A|=2[-4(-5)-0(2)]-(-6)[4(-5)-8(2)]+8[4(0)-8(-4)]=80

Report an Error

Example Question #96 : Matrices

Find the determinant of the matrix $A=\begin{vmatrix} -5&5 &-6 \\3 &-2 &8 \\2 &3 &1 \end{vmatrix}$

Possible Answers:

117

Correct answer:

117

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 $A=\begin{vmatrix} -5&5 &-6 \\3 &-2 &8 \\2 &3 &1 \end{vmatrix}$

The determinant is thus:

|A|=-5[-2(1)-3(8)]-5[3(1)-2(8)]+(-6)[3(3)-2(-2)]=117

Report an Error

Example Question #691 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 5&-5 &-3 \\-5 &5 &-7 \\7 &9 &5 \end{vmatrix}$

Possible Answers:

1551

972

223

800

Correct answer:

800

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 $A=\begin{vmatrix} 5&-5 &-3 \\-5 &5 &-7 \\7 &9 &5 \end{vmatrix}$

The determinant is thus:

|A|=5[5(5)-9(-7)]-(-5)[-5(5)-7(-7)]+(-3)[-5(9)-7(5)]=800

Report an Error

Example Question #692 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} -6& 0& 2\\8 &-8 &-8 \\8 &1 &0 \end{vmatrix}$

Possible Answers:

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 $A=\begin{vmatrix} -6& 0& 2\\8 &-8 &-8 \\8 &1 &0 \end{vmatrix}$

The determinant is thus:

|A|=-6[-8(0)-1(-8)]-0[8(0)-8(-8)]+2[8(1)-8(-8)]=96

Report an Error

Example Question #693 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 8& -2&5 \\ 8& 6& 5\\4 &7 &6 \end{vmatrix}$

Possible Answers:

1004

488

125

224

Correct answer:

224

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 $A=\begin{vmatrix} 8& -2&5 \\ 8& 6& 5\\4 &7 &6 \end{vmatrix}$

The determinant is thus:

|A|=8[6(6)-7(5)]-(-2)[8(6)-4(5)]+5[8(7)-4(6)]=224

Report an Error

Example Question #694 : Vectors And Vector Operations

Find the determinant of the matrix $A=\begin{vmatrix} 5& 8&-1 \\-2 &7 &-9 \\9 &5 &-1 \end{vmatrix}$

Possible Answers:

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 $A=\begin{vmatrix} 5& 8&-1 \\-2 &7 &-9 \\9 &5 &-1 \end{vmatrix}$

The determinant is thus:

|A|=5[7(-1)-5(-9)]-8[-2(-1)-9(-9)]+(-1)[-2(5)-9(7)]=-401

Report an Error

View Calculus 3 Tutors

Cole
Certified Tutor

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

View Calculus 3 Tutors

Ryanto
Certified Tutor

Excelsior College, Bachelor of Science, Business, General. University of Houston, Master of Science, Accounting.

View Calculus 3 Tutors

Joseph
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mathematics.

All Calculus 3 Resources

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

Popular Subjects

SSAT Tutors in Atlanta, Computer Science Tutors in Denver, Algebra Tutors in San Diego, MCAT Tutors in Seattle, GMAT Tutors in Chicago, Physics Tutors in Boston, Computer Science Tutors in New York City, ISEE Tutors in Denver, Algebra Tutors in Houston, Statistics Tutors in Boston

Popular Courses & Classes

LSAT Courses & Classes in New York City, GRE Courses & Classes in Washington DC, ISEE Courses & Classes in Washington DC, ISEE Courses & Classes in Chicago, LSAT Courses & Classes in Miami, ISEE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Chicago, GMAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Seattle, SSAT Courses & Classes in Washington DC

Popular Test Prep

SSAT Test Prep in Los Angeles, ACT Test Prep in Chicago, ISEE Test Prep in Chicago, SSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Denver, ACT Test Prep in New York City, ISEE Test Prep in Phoenix, ISEE Test Prep in Boston, LSAT Test Prep in New York City, GMAT Test Prep in Phoenix

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 #91 : Matrices

Example Question #92 : Matrices

Example Question #2681 : Calculus 3

Example Question #682 : Vectors And Vector Operations

Example Question #95 : Matrices

Example Question #96 : Matrices

Example Question #691 : Vectors And Vector Operations

Example Question #692 : Vectors And Vector Operations

Example Question #693 : Vectors And Vector Operations

Example Question #694 : 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: