Call Now to Set Up Tutoring:

(888) 888-0446

Linear Algebra : Symmetric Matrices

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 : Symmetric Matrices

Which matrix is symmetric?

Possible Answers:

$\begin{bmatrix} 1 &3 &-2 \\ 3& -2& 1\end{bmatrix}$

$\begin{bmatrix} 0 &1 \\0 &1 \end{bmatrix}$

$\begin{bmatrix} 1 &3 &-2 \\ 3& 6& 5\\-2 &5 & 0\end{bmatrix}$

$\begin{bmatrix} 1 &2 &1 \\2 &1 &5 \\1 &-5 &1 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 1 &3 &-2 \\ 3& 6& 5\\-2 &5 & 0\end{bmatrix}$

Explanation:

A symmetric matrix is symmetrical across the main diagonal. The numbers in the main diagonal can be anything, but the numbers in corresponding places on either side must be the same. In the correct answer, the matching numbers are the 3's, the -2's, and the 5's.

Report an Error

Example Question #2 : Symmetric Matrices

$\begin{align*}&\text{Select the symmetric matrix from the following choices:}\end{align*}$

Possible Answers:

$\begin{bmatrix}11&15&4\\23&12&-24\\12&-17&-12\end{bmatrix}$

$\begin{bmatrix}-3&13&23\\18&11&3\\19&9&-3\end{bmatrix}$

$\begin{bmatrix}-18&8&20\\8&-11&14\\20&14&3\end{bmatrix}$

$\begin{bmatrix}13&7&-18\\5&2&8\\-19&9&15\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-18&8&20\\8&-11&14\\20&14&3\end{bmatrix}$

Explanation:

$\begin{align*}&\text{A symmetric matrix is equal to its transpose, that is to say:}\\&A=A^{T}\\&\text{A transpose of a matrix is one in which the first row becomes the first column,}\\&\text{the second row the second column, and so on.}\\&\text{The symmetric matrix is:}\\&\begin{bmatrix}-18&8&20\\8&-11&14\\20&14&3\end{bmatrix}\end{align*}$

Report an Error

Example Question #3 : Symmetric Matrices

$\begin{align*}&\text{Which of the following matrices is symmetric?}\end{align*}$

Possible Answers:

$\begin{bmatrix}-19&-7&14\\-7&-7&2\\14&2&1\end{bmatrix}$

$\begin{bmatrix}-1&-13&-7\\-18&16&8\\-1&-13&-7\end{bmatrix}$

$\begin{bmatrix}-17&-36&-20\\-27&13&5\\-13&-2&-5\end{bmatrix}$

$\begin{bmatrix}15&6&15\\20&-16&20\\-13&-6&-13\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-19&-7&14\\-7&-7&2\\14&2&1\end{bmatrix}$

Explanation:

Report an Error

Example Question #4 : Symmetric Matrices

$\begin{align*}&\text{Which of the following matrices is symmetric?}\end{align*}$

Possible Answers:

$\begin{bmatrix}-9&9&16&-16&1&-7&3&28\\0&12&2&-4&-5&-7&-5&-8\\7&10&-4&-7&-17&-6&-5&-9\\-9&3&2&-18&15&27&-1&8\\-7&4&-8&6&25&-12&-10&-4\\1&1&1&18&-21&-6&23&5\\12&-14&4&-10&-2&14&-11&-35\\21&1&-18&1&-12&-4&-28&29\end{bmatrix}$

$\begin{bmatrix}-12&-16&-18&11&11&13&-20&1\\-16&-18&10&-1&-18&18&-16&6\\-18&10&4&-17&2&-14&-11&-16\\11&-1&-17&-1&-19&5&8&-20\\11&-18&2&-19&-13&8&5&-4\\13&18&-14&5&8&10&-19&19\\-20&-16&-11&8&5&-19&1&-3\\1&6&-16&-20&-4&19&-3&15\end{bmatrix}$

$\begin{bmatrix}8&7&-8&1&1&-8&7&8\\3&6&-15&-17&-17&-15&6&3\\12&-17&-16&6&6&-16&-17&12\\6&-15&-8&-3&-3&-8&-15&6\\8&-14&-8&-17&-17&-8&-14&8\\-2&-7&-3&-6&-6&-3&-7&-2\\-10&2&10&2&2&10&2&-10\\-6&-2&14&13&13&14&-2&-6\end{bmatrix}$

$\begin{bmatrix}6&12&10&7&-4&12&18&5\\11&7&13&16&19&13&-7&-13\\-4&-14&8&4&-3&-3&-9&18\\-16&-16&-7&16&-12&2&20&-17\\-16&-16&-7&16&-12&2&20&-17\\-4&-14&8&4&-3&-3&-9&18\\11&7&13&16&19&13&-7&-13\\6&12&10&7&-4&12&18&5\end{bmatrix}$

Correct answer:

Explanation:

$\begin{align*}&\text{A symmetric matrix is one that is equal to its transpose, i.e:}\\&A=A^{T}\\&\text{To review, a transpose of a matrix is one in which the first row becomes the first column,}\\&\text{the second row the second column, etc.}\\&\text{Therefore, the symmetric matrix is:}\\&\begin{bmatrix}-12&-16&-18&11&11&13&-20&1\\-16&-18&10&-1&-18&18&-16&6\\-18&10&4&-17&2&-14&-11&-16\\11&-1&-17&-1&-19&5&8&-20\\11&-18&2&-19&-13&8&5&-4\\13&18&-14&5&8&10&-19&19\\-20&-16&-11&8&5&-19&1&-3\\1&6&-16&-20&-4&19&-3&15\end{bmatrix}\end{align*}$

Report an Error

Example Question #5 : Symmetric Matrices

$\begin{align*}&\text{Choose the symmetric matrix from the four choices given:}\end{align*}$

Possible Answers:

$\begin{bmatrix}-3&-18&-19&32&-8\\-9&5&3&12&4\\-10&-5&12&-20&-10\\25&20&-11&-6&-7\\1&11&-1&2&-27\end{bmatrix}$

$\begin{bmatrix}13&6&-9&-6&18\\-15&-5&15&-19&4\\14&-6&9&-19&9\\-15&-5&15&-19&4\\13&6&-9&-6&18\end{bmatrix}$

$\begin{bmatrix}5&-5&13&-5&5\\8&-6&20&-6&8\\15&-6&5&-6&15\\7&19&-6&19&7\\-4&-16&-10&-16&-4\end{bmatrix}$

$\begin{bmatrix}-12&-16&-3&16&17\\-16&14&-7&-7&-4\\-3&-7&-11&7&-11\\16&-7&7&19&7\\17&-4&-11&7&-17\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-12&-16&-3&16&17\\-16&14&-7&-7&-4\\-3&-7&-11&7&-11\\16&-7&7&19&7\\17&-4&-11&7&-17\end{bmatrix}$

Explanation:

$\begin{align*}&\text{A symmetric matrix is one in which all values are mirrored across the diagonal. In other words}\text{it is equal to its transpose:}\\&A=A^{T}\\&\text{Recall that a transpose of a matrix is one in which the first row becomes the first column,}\\&\text{the second row the second column, etc.}\\&\begin{bmatrix}-12&-16&-3&16&17\\-16&14&-7&-7&-4\\-3&-7&-11&7&-11\\16&-7&7&19&7\\17&-4&-11&7&-17\end{bmatrix}\\&\text{Is a symmetric matrix.}\end{align*}$

Report an Error

Example Question #6 : Symmetric Matrices

$\begin{align*}&\text{Choose the symmetric matrix from the four choices given:}\end{align*}$

Possible Answers:

$\begin{bmatrix}13&14&-2&-20\\-14&16&7&-9\\-14&16&7&-9\\13&14&-2&-20\end{bmatrix}$

$\begin{bmatrix}3&12&23&-4\\4&12&-11&4\\14&-18&-8&-11\\-12&11&-2&-11\end{bmatrix}$

$\begin{bmatrix}-2&18&4&-12\\18&11&15&12\\4&15&-9&-4\\-12&12&-4&9\end{bmatrix}$

$\begin{bmatrix}-18&18&18&-18\\17&-2&-2&17\\9&7&7&9\\7&9&9&7\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-2&18&4&-12\\18&11&15&12\\4&15&-9&-4\\-12&12&-4&9\end{bmatrix}$

Explanation:

$\begin{align*}&\text{A symmetric matrix is one in which all values are mirrored across the diagonal. In other words}\text{it is equal to its transpose:}\\&A=A^{T}\\&\text{Recall that a transpose of a matrix is one in which the first row becomes the first column,}\\&\text{the second row the second column, etc.}\\&\begin{bmatrix}-2&18&4&-12\\18&11&15&12\\4&15&-9&-4\\-12&12&-4&9\end{bmatrix}\\&\text{Is a symmetric matrix.}\end{align*}$

Report an Error

Example Question #7 : Symmetric Matrices

$\begin{align*}&\text{Which of the following matrices is symmetric?}\end{align*}$

Possible Answers:

$\begin{bmatrix}-10&0&-17&-20&-13&18\\18&1&-11&-16&14&-15\\-16&-15&14&-9&11&-13\\-16&-15&14&-9&11&-13\\18&1&-11&-16&14&-15\\-10&0&-17&-20&-13&18\end{bmatrix}$

$\begin{bmatrix}-26&11&16&17&-4&-1\\20&-22&-2&9&8&-17\\24&7&-19&4&-19&2\\9&2&-4&8&21&5\\5&-1&-27&14&-14&-1\\6&-8&10&-3&-9&6\end{bmatrix}$

$\begin{bmatrix}-2&5&-10&-10&5&-2\\8&-3&-2&-2&-3&8\\5&-14&7&7&-14&5\\18&-17&-16&-16&-17&18\\-10&-4&-2&-2&-4&-10\\-11&-15&-13&-13&-15&-11\end{bmatrix}$

$\begin{bmatrix}-7&16&-4&18&4&1\\16&-6&3&9&11&18\\-4&3&-17&3&-18&-3\\18&9&3&0&4&1\\4&11&-18&4&-4&-6\\1&18&-3&1&-6&16\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-7&16&-4&18&4&1\\16&-6&3&9&11&18\\-4&3&-17&3&-18&-3\\18&9&3&0&4&1\\4&11&-18&4&-4&-6\\1&18&-3&1&-6&16\end{bmatrix}$

Explanation:

$\begin{align*}&\text{A symmetric matrix is one that is equal to its transpose, i.e:}\\&A=A^{T}\\&\text{To review, a transpose of a matrix is one in which the first row becomes the first column,}\\&\text{the second row the second column, etc.}\\&\text{Therefore, the symmetric matrix is:}\\&\begin{bmatrix}-7&16&-4&18&4&1\\16&-6&3&9&11&18\\-4&3&-17&3&-18&-3\\18&9&3&0&4&1\\4&11&-18&4&-4&-6\\1&18&-3&1&-6&16\end{bmatrix}\end{align*}$

Report an Error

Example Question #8 : Symmetric Matrices

$\begin{align*}&\text{Which of the following matrices is symmetric?}\end{align*}$

Possible Answers:

$\begin{bmatrix}-12&16&13&19&26&0&2\\24&5&-19&29&-19&16&-10\\21&-26&16&13&-17&16&7\\12&20&4&22&18&-3&-12\\17&-26&-9&10&-15&6&11\\-9&23&8&6&-3&8&8\\10&-18&0&-21&19&15&4\end{bmatrix}$

$\begin{bmatrix}18&8&19&-18&16&9&-1\\-13&12&13&17&-19&-13&15\\-15&-14&-19&-5&9&19&-8\\10&1&-9&-10&18&13&13\\-15&-14&-19&-5&9&19&-8\\-13&12&13&17&-19&-13&15\\18&8&19&-18&16&9&-1\end{bmatrix}$

$\begin{bmatrix}-3&1&-4&19&8&-5&20\\1&-4&-5&5&-11&0&19\\-4&-5&15&-11&20&-18&14\\19&5&-11&6&3&-9&-4\\8&-11&20&3&1&6&-4\\-5&0&-18&-9&6&2&20\\20&19&14&-4&-4&20&-15\end{bmatrix}$

$\begin{bmatrix}4&-16&6&-2&6&-16&4\\0&-11&3&3&3&-11&0\\12&2&-7&13&-7&2&12\\7&-13&-18&-17&-18&-13&7\\-10&-17&15&12&15&-17&-10\\19&0&18&-13&18&0&19\\-10&-20&2&-8&2&-20&-10\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-3&1&-4&19&8&-5&20\\1&-4&-5&5&-11&0&19\\-4&-5&15&-11&20&-18&14\\19&5&-11&6&3&-9&-4\\8&-11&20&3&1&6&-4\\-5&0&-18&-9&6&2&20\\20&19&14&-4&-4&20&-15\end{bmatrix}$

Explanation:

$\begin{align*}&\text{A symmetric matrix is one that is equal to its transpose, i.e:}\\&A=A^{T}\\&\text{To review, a transpose of a matrix is one in which the first row becomes the first column,}\\&\text{the second row the second column, etc.}\\&\text{Therefore, the symmetric matrix is:}\\&\begin{bmatrix}-3&1&-4&19&8&-5&20\\1&-4&-5&5&-11&0&19\\-4&-5&15&-11&20&-18&14\\19&5&-11&6&3&-9&-4\\8&-11&20&3&1&6&-4\\-5&0&-18&-9&6&2&20\\20&19&14&-4&-4&20&-15\end{bmatrix}\end{align*}$

Report an Error

Example Question #151 : Linear Algebra

$\begin{align*}&\text{Which of the following matrices is symmetric?}\end{align*}$

Possible Answers:

$\begin{bmatrix}17&10&13&-18&10&5&3\\10&-14&-7&5&-7&8&-8\\13&-7&20&1&15&-20&-7\\-18&5&1&-15&9&16&-6\\10&-7&15&9&18&-11&3\\5&8&-20&16&-11&-3&11\\3&-8&-7&-6&3&11&20\end{bmatrix}$

$\begin{bmatrix}15&14&-14&0&-14&14&15\\-7&13&-11&-13&-11&13&-7\\10&-12&18&11&18&-12&10\\18&-15&-5&-19&-5&-15&18\\-7&11&5&19&5&11&-7\\-3&8&14&4&14&8&-3\\-11&-7&14&-14&14&-7&-11\end{bmatrix}$

$\begin{bmatrix}14&19&-17&12&-2&-1&-14\\3&15&13&-4&13&3&-5\\-14&20&-4&8&-20&18&12\\-7&16&5&13&12&-11&-9\\-14&20&-4&8&-20&18&12\\3&15&13&-4&13&3&-5\\14&19&-17&12&-2&-1&-14\end{bmatrix}$

$\begin{bmatrix}-21&-16&14&-5&-2&17&-20\\-23&-1&-20&-19&25&-25&-2\\22&-13&-3&-12&-19&2&9\\2&-26&-5&-12&10&-26&-16\\-10&17&-11&2&5&30&-11\\25&-16&-5&-18&21&18&2\\-27&5&17&-9&-3&10&1\end{bmatrix}$

Correct answer:

$\begin{bmatrix}17&10&13&-18&10&5&3\\10&-14&-7&5&-7&8&-8\\13&-7&20&1&15&-20&-7\\-18&5&1&-15&9&16&-6\\10&-7&15&9&18&-11&3\\5&8&-20&16&-11&-3&11\\3&-8&-7&-6&3&11&20\end{bmatrix}$

Explanation:

$\begin{align*}&\text{A symmetric matrix is one that is equal to its transpose, i.e:}\\&A=A^{T}\\&\text{To review, a transpose of a matrix is one in which the first row becomes the first column,}\\&\text{the second row the second column, etc.}\\&\text{Therefore, the symmetric matrix is:}\\&\begin{bmatrix}17&10&13&-18&10&5&3\\10&-14&-7&5&-7&8&-8\\13&-7&20&1&15&-20&-7\\-18&5&1&-15&9&16&-6\\10&-7&15&9&18&-11&3\\5&8&-20&16&-11&-3&11\\3&-8&-7&-6&3&11&20\end{bmatrix}\end{align*}$

Report an Error

Example Question #152 : Linear Algebra

$\begin{align*}&\text{Which of the following matrices is symmetric?}\end{align*}$

Possible Answers:

$\begin{bmatrix}10&-34&2&14&-4\\-25&19&2&5&-13\\-5&-6&1&-15&-35\\5&-4&-7&24&1\\3&-6&-26&9&-2\end{bmatrix}$

$\begin{bmatrix}-13&6&13&2&-17\\6&19&17&14&-7\\13&17&7&-10&-13\\2&14&-10&-6&-15\\-17&-7&-13&-15&4\end{bmatrix}$

$\begin{bmatrix}3&-19&-10&-18&-16\\9&16&-19&-8&-7\\-9&-2&17&8&-15\\9&16&-19&-8&-7\\3&-19&-10&-18&-16\end{bmatrix}$

$\begin{bmatrix}5&19&8&19&5\\13&-9&-8&-9&13\\3&-15&17&-15&3\\16&-16&-7&-16&16\\12&-20&3&-20&12\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-13&6&13&2&-17\\6&19&17&14&-7\\13&17&7&-10&-13\\2&14&-10&-6&-15\\-17&-7&-13&-15&4\end{bmatrix}$

Explanation:

$\begin{align*}&\text{A symmetric matrix is one that is equal to its transpose, i.e:}\\&A=A^{T}\\&\text{To review, a transpose of a matrix is one in which the first row becomes the first column,}\\&\text{the second row the second column, etc.}\\&\text{Therefore, the symmetric matrix is:}\\&\begin{bmatrix}-13&6&13&2&-17\\6&19&17&14&-7\\13&17&7&-10&-13\\2&14&-10&-6&-15\\-17&-7&-13&-15&4\end{bmatrix}\end{align*}$

Report an Error

View Linear Algebra Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View Linear Algebra Tutors

Pritam
Certified Tutor

University of Washington-Seattle Campus, Bachelor of Engineering, Electrical Engineering.

View Linear Algebra Tutors

Scott
Certified Tutor

Florida State University, Bachelor of Science, Applied Mathematics. Florida State University, Bachelor of Science, Astrophysi...

All Linear Algebra Resources

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

Popular Subjects

English Tutors in Philadelphia, SSAT Tutors in Houston, SSAT Tutors in Chicago, Chemistry Tutors in Philadelphia, Math Tutors in New York City, Math Tutors in Seattle, Calculus Tutors in San Francisco-Bay Area, LSAT Tutors in Miami, Chemistry Tutors in Chicago, Biology Tutors in San Diego

Popular Courses & Classes

GRE Courses & Classes in Washington DC, ACT Courses & Classes in Denver, LSAT Courses & Classes in Houston, Spanish Courses & Classes in Washington DC, SSAT Courses & Classes in New York City, MCAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Boston, LSAT Courses & Classes in Seattle, ISEE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Seattle

Popular Test Prep

SAT Test Prep in Philadelphia, SAT Test Prep in Chicago, ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in San Diego, GRE Test Prep in San Francisco-Bay Area, ACT Test Prep in Seattle, GMAT Test Prep in New York City, LSAT Test Prep in San Francisco-Bay Area, GRE Test Prep in San Diego, ACT Test Prep in Denver

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 : Symmetric Matrices

Study concepts, example questions & explanations for Linear Algebra

All Linear Algebra Resources

Example Questions

Example Question #1 : Symmetric Matrices

Example Question #2 : Symmetric Matrices

Example Question #3 : Symmetric Matrices

Example Question #4 : Symmetric Matrices

Example Question #5 : Symmetric Matrices

Example Question #6 : Symmetric Matrices

Example Question #7 : Symmetric Matrices

Example Question #8 : Symmetric Matrices

Example Question #151 : Linear Algebra

Example Question #152 : Linear Algebra

All Linear Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: