We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Linear Algebra : Linear Algebra

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 : The Transpose

Find the transpose of matrix A.

$A=\begin{bmatrix} 2& 4&6 &8 \\1 & 3& 5&7 \end{bmatrix}$

Possible Answers:

$A^{T}=\begin{bmatrix} 1&5 \\2 & 6\\ 3&7 \\ 4&8 \end{bmatrix}$

$A^{T}=\begin{bmatrix} 1& 2\\ 3& 4\\ 5& 6\\7 & 8\end{bmatrix}$

$A^{T}=\begin{bmatrix} 2&1 \\ 4&3 \\6 &5 \\ 8&7 \end{bmatrix}$

None of the other answers

$A^{T}=\begin{bmatrix} 1& 3&5 &7 \\ 2& 4&6 &8 \end{bmatrix}$

Correct answer:

$A^{T}=\begin{bmatrix} 2&1 \\ 4&3 \\6 &5 \\ 8&7 \end{bmatrix}$

Explanation:

For a 2x4 matrix A, the transpose of A is a 4x2 matrix, where the columns are formed from the corresponding rows of A.

Report an Error

Example Question #111 : Linear Algebra

$\begin{align*}&\text{Find the transpose of }A=\begin{bmatrix}-15&3\\-2&18\end{bmatrix}\end{align*}$

Possible Answers:

$\begin{bmatrix}18&3\\-2&-15\end{bmatrix}$

$\begin{bmatrix}3&18\\-15&-2\end{bmatrix}$

$\begin{bmatrix}-2&-15\\18&3\end{bmatrix}$

$\begin{bmatrix}-15&-2\\3&18\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-15&-2\\3&18\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Determining the transpose of a matrix is relatively simple, though attention to detail should be exercised.}\\&\text{In creating the transpose, the first row becomes the first column, the second row the second column, etc:}\\&A=\begin{bmatrix}-15&3\\-2&18\end{bmatrix}\\&A^{T}=\begin{bmatrix}-15&-2\\3&18\end{bmatrix}\end{align*}$

Report an Error

Example Question #112 : Linear Algebra

$\begin{align*}&\text{Find the transpose of }\begin{bmatrix}1&2\\-2&-6\\-8&-20\\-18&-14\\16&15\\20&3\end{bmatrix}^{T}\end{align*}$

Possible Answers:

$\begin{bmatrix}3&15&-14&-20&-6&2\\20&16&-18&-8&-2&1\end{bmatrix}$

$\begin{bmatrix}1&-2&-8&-18&16&20\\2&-6&-20&-14&15&3\end{bmatrix}$

$\begin{bmatrix}20&16&-18&-8&-2&1\\3&15&-14&-20&-6&2\end{bmatrix}$

$\begin{bmatrix}1&2\\-2&-6\\-8&-20\\-18&-14\\16&15\\20&3\end{bmatrix}$

Correct answer:

$\begin{bmatrix}1&2\\-2&-6\\-8&-20\\-18&-14\\16&15\\20&3\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Note the superscript, T, in our problem statement; this denotes the transpose.}\\&\text{The transpose of the transpose of a matrix is the orignal matrix, so:}\\&\begin{bmatrix}1&2\\-2&-6\\-8&-20\\-18&-14\\16&15\\20&3\end{bmatrix}^{TT}=\begin{bmatrix}1&2\\-2&-6\\-8&-20\\-18&-14\\16&15\\20&3\end{bmatrix}\end{align*}$

Report an Error

Example Question #113 : Linear Algebra

$\begin{align*}&\text{Find }\begin{bmatrix}1&-1&0\\3&13&-10\end{bmatrix}^{T}\end{align*}$

Possible Answers:

$\begin{bmatrix}0&-10\\-1&13\\1&3\end{bmatrix}$

$\begin{bmatrix}-10&0\\13&-1\\3&1\end{bmatrix}$

$\begin{bmatrix}1&3\\-1&13\\0&-10\end{bmatrix}$

$\begin{bmatrix}3&1\\13&-1\\-10&0\end{bmatrix}$

Correct answer:

$\begin{bmatrix}1&3\\-1&13\\0&-10\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Superscript T denotes the transpose of a matrix. Finding this transpose requies only}\\&\text{treating the first row as the first column, the second as row the second column, etc:}\\&\begin{bmatrix}1&-1&0\\3&13&-10\end{bmatrix}^{T}=\begin{bmatrix}1&3\\-1&13\\0&-10\end{bmatrix}\end{align*}$

Report an Error

Example Question #114 : Linear Algebra

$\begin{align*}&\text{Find the transpose of }A=\begin{bmatrix}-13&-12&15&1&-18\\0&3&-17&-1&-13\end{bmatrix}\end{align*}$

Possible Answers:

$\begin{bmatrix}0&-13\\3&-12\\-17&15\\-1&1\\-13&-18\end{bmatrix}$

$\begin{bmatrix}-13&-18\\-1&1\\-17&15\\3&-12\\0&-13\end{bmatrix}$

$\begin{bmatrix}-13&0\\-12&3\\15&-17\\1&-1\\-18&-13\end{bmatrix}$

$\begin{bmatrix}-18&-13\\1&-1\\15&-17\\-12&3\\-13&0\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-13&0\\-12&3\\15&-17\\1&-1\\-18&-13\end{bmatrix}$

Explanation:

Report an Error

Example Question #15 : The Transpose

$\begin{align*}&\text{Find the transpose of }A=\begin{bmatrix}10&20&2&-7&13&-3&11&-8\\-6&13&-13&0&3&6&4&-13\\-19&5&-14&-10&-12&-16&12&-12\\-12&-18&-13&-18&-17&-15&8&-2\\-2&-14&0&13&-19&-6&-15&-2\\-17&16&1&-16&-15&-9&-14&-4\end{bmatrix}\end{align*}$

Possible Answers:

$\begin{bmatrix}-4&-2&-2&-12&-13&-8\\-14&-15&8&12&4&11\\-9&-6&-15&-16&6&-3\\-15&-19&-17&-12&3&13\\-16&13&-18&-10&0&-7\\1&0&-13&-14&-13&2\\16&-14&-18&5&13&20\\-17&-2&-12&-19&-6&10\end{bmatrix}$

$\begin{bmatrix}-17&-2&-12&-19&-6&10\\16&-14&-18&5&13&20\\1&0&-13&-14&-13&2\\-16&13&-18&-10&0&-7\\-15&-19&-17&-12&3&13\\-9&-6&-15&-16&6&-3\\-14&-15&8&12&4&11\\-4&-2&-2&-12&-13&-8\end{bmatrix}$

$\begin{bmatrix}-8&-13&-12&-2&-2&-4\\11&4&12&8&-15&-14\\-3&6&-16&-15&-6&-9\\13&3&-12&-17&-19&-15\\-7&0&-10&-18&13&-16\\2&-13&-14&-13&0&1\\20&13&5&-18&-14&16\\10&-6&-19&-12&-2&-17\end{bmatrix}$

$\begin{bmatrix}10&-6&-19&-12&-2&-17\\20&13&5&-18&-14&16\\2&-13&-14&-13&0&1\\-7&0&-10&-18&13&-16\\13&3&-12&-17&-19&-15\\-3&6&-16&-15&-6&-9\\11&4&12&8&-15&-14\\-8&-13&-12&-2&-2&-4\end{bmatrix}$

Correct answer:

$\begin{bmatrix}10&-6&-19&-12&-2&-17\\20&13&5&-18&-14&16\\2&-13&-14&-13&0&1\\-7&0&-10&-18&13&-16\\13&3&-12&-17&-19&-15\\-3&6&-16&-15&-6&-9\\11&4&12&8&-15&-14\\-8&-13&-12&-2&-2&-4\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Determining the transpose of a matrix is relatively simple,}\\&\text{though attention to detail should be exercised.}\\&\text{In creating the transpose, the first row becomes the first column,}\\&\text{the second row the second column, etc:}\\&A=\begin{bmatrix}10&20&2&-7&13&-3&11&-8\\-6&13&-13&0&3&6&4&-13\\-19&5&-14&-10&-12&-16&12&-12\\-12&-18&-13&-18&-17&-15&8&-2\\-2&-14&0&13&-19&-6&-15&-2\\-17&16&1&-16&-15&-9&-14&-4\end{bmatrix}\\&A^{T}=\begin{bmatrix}10&-6&-19&-12&-2&-17\\20&13&5&-18&-14&16\\2&-13&-14&-13&0&1\\-7&0&-10&-18&13&-16\\13&3&-12&-17&-19&-15\\-3&6&-16&-15&-6&-9\\11&4&12&8&-15&-14\\-8&-13&-12&-2&-2&-4\end{bmatrix}\end{align*}$

Report an Error

Example Question #115 : Linear Algebra

$\begin{align*}&\text{Find }A^{T}\text{ for }A=\begin{bmatrix}5&-16&2\\-4&-15&20\\8&-1&11\\8&-11&-15\\17&20&-9\end{bmatrix}\end{align*}$

Possible Answers:

$\begin{bmatrix}2&20&11&-15&-9\\-16&-15&-1&-11&20\\5&-4&8&8&17\end{bmatrix}$

$\begin{bmatrix}17&8&8&-4&5\\20&-11&-1&-15&-16\\-9&-15&11&20&2\end{bmatrix}$

$\begin{bmatrix}5&-4&8&8&17\\-16&-15&-1&-11&20\\2&20&11&-15&-9\end{bmatrix}$

$\begin{bmatrix}-9&-15&11&20&2\\20&-11&-1&-15&-16\\17&8&8&-4&5\end{bmatrix}$

Correct answer:

$\begin{bmatrix}5&-4&8&8&17\\-16&-15&-1&-11&20\\2&20&11&-15&-9\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Finding the transpose of a matrix is simply a matter of making}\\&\text{the first row the first column, the second row the second column, etc:}\\&A=\begin{bmatrix}5&-16&2\\-4&-15&20\\8&-1&11\\8&-11&-15\\17&20&-9\end{bmatrix}\\&A^{T}=\begin{bmatrix}5&-4&8&8&17\\-16&-15&-1&-11&20\\2&20&11&-15&-9\end{bmatrix}\end{align*}$

Report an Error

Example Question #31 : Operations And Properties

$\begin{align*}&\text{Find the transpose of }\begin{bmatrix}6&-14\\14&8\\15&-15\\18&-16\\-5&20\\-7&13\end{bmatrix}^{T}\end{align*}$

Possible Answers:

$\begin{bmatrix}-7&-5&18&15&14&6\\13&20&-16&-15&8&-14\end{bmatrix}$

$\begin{bmatrix}6&14&15&18&-5&-7\\-14&8&-15&-16&20&13\end{bmatrix}$

$\begin{bmatrix}13&20&-16&-15&8&-14\\-7&-5&18&15&14&6\end{bmatrix}$

$\begin{bmatrix}6&-14\\14&8\\15&-15\\18&-16\\-5&20\\-7&13\end{bmatrix}$

Correct answer:

$\begin{bmatrix}6&-14\\14&8\\15&-15\\18&-16\\-5&20\\-7&13\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Note the superscript, T, in our problem statement; this denotes the transpose.}\\&\text{The transpose of the transpose of a matrix is the orignal matrix, so:}\\&\begin{bmatrix}6&-14\\14&8\\15&-15\\18&-16\\-5&20\\-7&13\end{bmatrix}^{TT}=\begin{bmatrix}6&-14\\14&8\\15&-15\\18&-16\\-5&20\\-7&13\end{bmatrix}\end{align*}$

Report an Error

Example Question #41 : Operations And Properties

$\begin{align*}&\text{Find the transpose of }\begin{bmatrix}-4&-4&13&-8&13\\-6&-17&18&12&3\\1&-9&-6&-7&18\\18&-17&-18&-7&6\end{bmatrix}^{T}\end{align*}$

Possible Answers:

$\begin{bmatrix}6&18&3&13\\-7&-7&12&-8\\-18&-6&18&13\\-17&-9&-17&-4\\18&1&-6&-4\end{bmatrix}$

$\begin{bmatrix}-4&-4&13&-8&13\\-6&-17&18&12&3\\1&-9&-6&-7&18\\18&-17&-18&-7&6\end{bmatrix}$

$\begin{bmatrix}-4&-6&1&18\\-4&-17&-9&-17\\13&18&-6&-18\\-8&12&-7&-7\\13&3&18&6\end{bmatrix}$

$\begin{bmatrix}18&1&-6&-4\\-17&-9&-17&-4\\-18&-6&18&13\\-7&-7&12&-8\\6&18&3&13\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-4&-4&13&-8&13\\-6&-17&18&12&3\\1&-9&-6&-7&18\\18&-17&-18&-7&6\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Note the superscript, T, in our problem statement; this denotes the transpose.}\\&\text{The transpose of the transpose of a matrix is the orignal matrix, so:}\\&\begin{bmatrix}-4&-4&13&-8&13\\-6&-17&18&12&3\\1&-9&-6&-7&18\\18&-17&-18&-7&6\end{bmatrix}^{TT}=\begin{bmatrix}-4&-4&13&-8&13\\-6&-17&18&12&3\\1&-9&-6&-7&18\\18&-17&-18&-7&6\end{bmatrix}\end{align*}$

Report an Error

Example Question #42 : Operations And Properties

$\begin{align*}&\text{Find }A^{T}\text{ for }A=\begin{bmatrix}-11&14\\-18&7\\7&-6\\-17&-9\end{bmatrix}\end{align*}$

Possible Answers:

$\begin{bmatrix}14&7&-6&-9\\-11&-18&7&-17\end{bmatrix}$

$\begin{bmatrix}-17&7&-18&-11\\-9&-6&7&14\end{bmatrix}$

$\begin{bmatrix}-11&-18&7&-17\\14&7&-6&-9\end{bmatrix}$

$\begin{bmatrix}-9&-6&7&14\\-17&7&-18&-11\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-11&-18&7&-17\\14&7&-6&-9\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Finding the transpose of a matrix is simply a matter of making}\\&\text{the first row the first column, the second row the second column, etc:}\\&A=\begin{bmatrix}-11&14\\-18&7\\7&-6\\-17&-9\end{bmatrix}\\&A^{T}=\begin{bmatrix}-11&-18&7&-17\\14&7&-6&-9\end{bmatrix}\end{align*}$

Report an Error

View Linear Algebra Tutors

James
Certified Tutor

Purdue University-Main Campus, Doctor of Education, Mathematics Teacher Education.

View Linear Algebra Tutors

Pedro
Certified Tutor

Harvard University, Bachelor of Chemistry, Chemistry.

View Linear Algebra Tutors

Nafis
Certified Tutor

University of Leipzig, Germany., Bachelor of Science, Physics. University of Pittsburgh-Pittsburgh Campus, Doctor of Philosop...

All Linear Algebra Resources

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

Popular Subjects

Reading Tutors in Los Angeles, Reading Tutors in New York City, Biology Tutors in San Francisco-Bay Area, French Tutors in San Francisco-Bay Area, Algebra Tutors in Miami, Computer Science Tutors in Dallas Fort Worth, Statistics Tutors in Denver, Calculus Tutors in San Francisco-Bay Area, French Tutors in New York City, Spanish Tutors in New York City

Popular Courses & Classes

ISEE Courses & Classes in Atlanta, GRE Courses & Classes in Denver, GRE Courses & Classes in Houston, GMAT Courses & Classes in Chicago, GMAT Courses & Classes in Denver, LSAT Courses & Classes in Washington DC, GRE Courses & Classes in San Diego, LSAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Phoenix, SAT Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in Houston, MCAT Test Prep in Boston, ACT Test Prep in Phoenix, SSAT Test Prep in Atlanta, MCAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Chicago, LSAT Test Prep in Denver, SAT Test Prep in San Diego, GRE Test Prep in Houston, SSAT 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

Linear Algebra : Linear Algebra

Study concepts, example questions & explanations for Linear Algebra

All Linear Algebra Resources

Example Questions

Example Question #1 : The Transpose

Example Question #111 : Linear Algebra

Example Question #112 : Linear Algebra

Example Question #113 : Linear Algebra

Example Question #114 : Linear Algebra

Example Question #15 : The Transpose

Example Question #115 : Linear Algebra

Example Question #31 : Operations And Properties

Example Question #41 : Operations And Properties

Example Question #42 : Operations And Properties

All Linear Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: