We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Linear Algebra : Row Operations and Equivalent Systems

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 #71 : Linear Equations

$\begin{align*}&\text{Identify the matrix which is not a equivalent to:}\\&\begin{bmatrix}19&6&-10\\-1&-12&7\\\end{bmatrix}\end{align*}$

Possible Answers:

$\begin{bmatrix}22&9&-7\\2&-9&10\\\end{bmatrix}$

$\begin{bmatrix}\frac{19}{2}&3&-5\\\frac{1}{6}&2&-\frac{7}{6}\\\end{bmatrix}$

$\begin{bmatrix}-38&-12&20\\2&24&-14\\\end{bmatrix}$

$\begin{bmatrix}20&18&-17\\-1&-12&7\\\end{bmatrix}$

Correct answer:

$\begin{bmatrix}22&9&-7\\2&-9&10\\\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Two matrices are equivalent if one can be turned into another}\\&\text{via row operations: scaling a row by multiplication of some}\\&\text{constant, addition/subtraction of one row with another, or a}\\&\text{combination of these processes.}\\&\text{The matrix: }\begin{bmatrix}-38&-12&20\\2&24&-14\\\end{bmatrix}\text{ is our entire initial matrix scaled by }-2.\\&\text{The matrix }\begin{bmatrix}\frac{19}{2}&3&-5\\\frac{1}{6}&2&-\frac{7}{6}\\\end{bmatrix}\text{ can be formed by scaling the first and second rows of}\\&\text{the orignal by }\frac{1}{2}\text{ and }-\frac{1}{6}.\\&\text{Finally, subtracting one row from another creates }\begin{bmatrix}20&18&-17\\-1&-12&7\\\end{bmatrix}.\\&\text{No row operations, however, will create }\begin{bmatrix}22&9&-7\\2&-9&10\\\end{bmatrix}.\end{align*}$

Report an Error

Example Question #72 : Linear Equations

$\begin{align*}&\text{Among the choices given, find the matrix that is not }A=\begin{bmatrix}17&4&-2&7\\-5&14&19&-15\\\end{bmatrix}\\&\text{in an equivalent configuration.}\end{align*}$

Possible Answers:

$\begin{bmatrix}34&8&-4&14\\-30&84&114&-90\\\end{bmatrix}$

$\begin{bmatrix}-68&-16&8&-28\\20&-56&-76&60\\\end{bmatrix}$

$\begin{bmatrix}22&-10&-21&22\\-5&14&19&-15\\\end{bmatrix}$

$\begin{bmatrix}18&5&-1&8\\-4&15&20&-14\\\end{bmatrix}$

Correct answer:

$\begin{bmatrix}18&5&-1&8\\-4&15&20&-14\\\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Two matrices are equivalent if one can be turned into another}\\&\text{via row operations: scaling a row by multiplication of some}\\&\text{constant, addition/subtraction of one row with another, or a}\\&\text{combination of these processes.}\\&\text{The matrix: }\begin{bmatrix}-68&-16&8&-28\\20&-56&-76&60\\\end{bmatrix}\text{ is our entire initial matrix scaled by }-4.\\&\text{The matrix }\begin{bmatrix}34&8&-4&14\\-30&84&114&-90\\\end{bmatrix}\text{ can be formed by scaling the first and second rows of}\\&\text{the orignal by }2\text{ and }6.\\&\text{Finally, subtracting one row from another creates }\begin{bmatrix}22&-10&-21&22\\-5&14&19&-15\\\end{bmatrix}.\\&\text{No row operations, however, will create }\begin{bmatrix}18&5&-1&8\\-4&15&20&-14\\\end{bmatrix}.\end{align*}$

Report an Error

Example Question #73 : Linear Equations

$\begin{align*}&\text{Which of the following matrices is not equivalent to}\\&\begin{bmatrix}2&10&20\\6&6&-11\\\end{bmatrix}?\end{align*}$

Possible Answers:

$\begin{bmatrix}8&40&80\\24&24&-44\\\end{bmatrix}$

$\begin{bmatrix}-4&4&31\\6&6&-11\\\end{bmatrix}$

$\begin{bmatrix}1&9&19\\5&5&-12\\\end{bmatrix}$

$\begin{bmatrix}-\frac{2}{3}&-\frac{10}{3}&-\frac{20}{3}\\\frac{3}{2}&\frac{3}{2}&-\frac{11}{4}\\\end{bmatrix}$

Correct answer:

$\begin{bmatrix}1&9&19\\5&5&-12\\\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Two matrices are equivalent if one can be turned into another}\\&\text{via row operations: scaling a row by multiplication of some}\\&\text{constant, addition/subtraction of one row with another, or a}\\&\text{combination of these processes.}\\&\text{The matrix: }\begin{bmatrix}8&40&80\\24&24&-44\\\end{bmatrix}\text{ is our entire initial matrix scaled by }4.\\&\text{The matrix }\begin{bmatrix}-\frac{2}{3}&-\frac{10}{3}&-\frac{20}{3}\\\frac{3}{2}&\frac{3}{2}&-\frac{11}{4}\\\end{bmatrix}\text{ can be formed by scaling the first and second rows of}\\&\text{the orignal by }-\frac{1}{3}\text{ and }\frac{1}{4}.\\&\text{Finally, subtracting one row from another creates }\begin{bmatrix}-4&4&31\\6&6&-11\\\end{bmatrix}.\\&\text{No row operations, however, will create }\begin{bmatrix}1&9&19\\5&5&-12\\\end{bmatrix}.\end{align*}$

Report an Error

Example Question #74 : Linear Equations

$\begin{align*}&\text{Among the choices given, find the matrix that is not }A=\begin{bmatrix}-13&-15&16&-14\\8&16&-13&3\\\end{bmatrix}\\&\text{in an equivalent configuration.}\end{align*}$

Possible Answers:

$\begin{bmatrix}-\frac{13}{3}&-5&\frac{16}{3}&-\frac{14}{3}\\-32&-64&52&-12\\\end{bmatrix}$

$\begin{bmatrix}52&60&-64&56\\-32&-64&52&-12\\\end{bmatrix}$

$\begin{bmatrix}-16&-18&13&-17\\5&13&-16&0\\\end{bmatrix}$

$\begin{bmatrix}-21&-31&29&-17\\8&16&-13&3\\\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-16&-18&13&-17\\5&13&-16&0\\\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Two matrices are equivalent if one can be turned into another}\\&\text{via row operations: scaling a row by multiplication of some}\\&\text{constant, addition/subtraction of one row with another, or a}\\&\text{combination of these processes.}\\&\text{The matrix: }\begin{bmatrix}52&60&-64&56\\-32&-64&52&-12\\\end{bmatrix}\text{ is our entire initial matrix scaled by }-4.\\&\text{The matrix }\begin{bmatrix}-\frac{13}{3}&-5&\frac{16}{3}&-\frac{14}{3}\\-32&-64&52&-12\\\end{bmatrix}\text{ can be formed by scaling the first and second rows of}\\&\text{the orignal by }\frac{1}{3}\text{ and }-4.\\&\text{Finally, subtracting one row from another creates }\begin{bmatrix}-21&-31&29&-17\\8&16&-13&3\\\end{bmatrix}.\\&\text{No row operations, however, will create }\begin{bmatrix}-16&-18&13&-17\\5&13&-16&0\\\end{bmatrix}.\end{align*}$

Report an Error

Example Question #75 : Linear Equations

$\begin{align*}&\text{Which of the following matrices is not equivalent to}\\&\begin{bmatrix}-3&-7&-15\\15&-15&18\\\end{bmatrix}?\end{align*}$

Possible Answers:

$\begin{bmatrix}-2&-6&-14\\16&-14&19\\\end{bmatrix}$

$\begin{bmatrix}-1&-\frac{7}{3}&-5\\-60&60&-72\\\end{bmatrix}$

$\begin{bmatrix}9&21&45\\-45&45&-54\\\end{bmatrix}$

$\begin{bmatrix}-3&-7&-15\\18&-8&33\\\end{bmatrix}$

Correct answer:

$\begin{bmatrix}-2&-6&-14\\16&-14&19\\\end{bmatrix}$

Explanation:

$\begin{align*}&\text{Two matrices are equivalent if one can be turned into another}\\&\text{via row operations: scaling a row by multiplication of some}\\&\text{constant, addition/subtraction of one row with another, or a}\\&\text{combination of these processes.}\\&\text{The matrix: }\begin{bmatrix}9&21&45\\-45&45&-54\\\end{bmatrix}\text{ is our entire initial matrix scaled by }-3.\\&\text{The matrix }\begin{bmatrix}-1&-\frac{7}{3}&-5\\-60&60&-72\\\end{bmatrix}\text{ can be formed by scaling the first and second rows of}\\&\text{the orignal by }\frac{1}{3}\text{ and }-4.\\&\text{Finally, subtracting one row from another creates }\begin{bmatrix}-3&-7&-15\\18&-8&33\\\end{bmatrix}.\\&\text{No row operations, however, will create }\begin{bmatrix}-2&-6&-14\\16&-14&19\\\end{bmatrix}.\end{align*}$

Report an Error

View Linear Algebra Tutors

Robert
Certified Tutor

University of Pittsburgh, Bachelor of Science, Physics.

View Linear Algebra Tutors

Muhammad
Certified Tutor

Quaid-E-Azam University, Master of Science, Applied Mathematics. Quaid-E-Azam University, Master of Philosophy, Applied Lingu...

View Linear Algebra Tutors

Diana
Certified Tutor

San Diego State University, Bachelor of Engineering, Electrical Engineering. Georgetown University, Masters in Business Admin...

All Linear Algebra Resources

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

Popular Subjects

SAT Tutors in Los Angeles, Biology Tutors in Houston, GMAT Tutors in San Diego, Calculus Tutors in San Diego, ACT Tutors in Houston, Physics Tutors in Chicago, Spanish Tutors in Denver, ACT Tutors in Dallas Fort Worth, GRE Tutors in Chicago, MCAT Tutors in Philadelphia

Popular Courses & Classes

ACT Courses & Classes in Houston, MCAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in San Diego, ACT Courses & Classes in Miami, ACT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Houston, MCAT Courses & Classes in Washington DC, ACT Courses & Classes in Philadelphia, LSAT Courses & Classes in Boston, SSAT Courses & Classes in New York City

Popular Test Prep

MCAT Test Prep in Phoenix, SAT Test Prep in Philadelphia, MCAT Test Prep in Houston, GRE Test Prep in Washington DC, ACT Test Prep in Phoenix, LSAT Test Prep in Los Angeles, LSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Houston, SAT Test Prep in Washington DC, GMAT Test Prep in New York City

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 : Row Operations and Equivalent Systems

Study concepts, example questions & explanations for Linear Algebra

All Linear Algebra Resources

Example Questions

Example Question #71 : Linear Equations

Example Question #72 : Linear Equations

Example Question #73 : Linear Equations

Example Question #74 : Linear Equations

Example Question #75 : Linear Equations

All Linear Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: