We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Linear Algebra : Criteria for Uniqueness and Consistency

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 : Criteria For Uniqueness And Consistency

$\begin{align*}&\text{Decide if there is a unique solution for the equation: }\\&\begin{bmatrix}-6&-7&-19\\-8&19&-14\\0&5&2\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}-21\\-36\\-149\end{bmatrix}\end{align*}$

Possible Answers:

$\text{There is a unique solution.}$

$\text{There is not a unique solution.}$

Correct answer:

$\text{There is not a unique solution.}$

Explanation:

$\begin{align*}&\text{To determine whether or not the system of equations represented}\\&\text{by a matrix equation has a unique solution, one should calculate}\\&\text{the determinant. If the determinant is a nonzero value, then}\\&\text{the system of equations has a unique solution. Otherwise, if}\\&\text{the determinant is zero, the system of equation may have no}\\&\text{solution, or it may have an infinite number of them. To refresh,}\\&\text{to calculate a matrix of the given dimensions we use the formula:}\\&det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)\\&det\begin{bmatrix}-6&-7&-19\\-8&19&-14\\0&5&2\end{bmatrix}=0\\&\text{There is not a unique solution.}\end{align*}$

Report an Error

Example Question #671 : Linear Algebra

$\begin{align*}&\text{Is there a unique solution for the equation }\\&\begin{bmatrix}-20&12\\7&16\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-171\\149\end{bmatrix}?\end{align*}$

Possible Answers:

$\text{There is a unique solution.}$

$\text{There is not a unique solution.}$

Correct answer:

$\text{There is a unique solution.}$

Explanation:

$\begin{align*}&\text{To determine whether or not the system of equations represented}\\&\text{by a matrix equation has a unique solution, one should calculate}\\&\text{the determinant. If the determinant is a nonzero value, then}\\&\text{the system of equations has a unique solution. Otherwise, if}\\&\text{the determinant is zero, the system of equation may have no}\\&\text{solution, or it may have an infinite number of them. To refresh,}\\&\text{to calculate a matrix of the given dimensions we use the formula:}\\&det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc\\&det\begin{bmatrix}-20&12\\7&16\end{bmatrix}=-404\\&\text{There is a unique solution.}\end{align*}$

Report an Error

Example Question #672 : Linear Algebra

$\begin{align*}&\text{Determine whether or not the equation }\\&\begin{bmatrix}6&-8\\3&12\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-188\\-101\end{bmatrix}\\&\text{has a unique solution.}\end{align*}$

Possible Answers:

$\text{There is not a unique solution.}$

$\text{There is a unique solution.}$

Correct answer:

$\text{There is a unique solution.}$

Explanation:

$\begin{align*}&\text{To determine whether or not the system of equations represented}\\&\text{by a matrix equation has a unique solution, one should calculate}\\&\text{the determinant. If the determinant is a nonzero value, then}\\&\text{the system of equations has a unique solution. Otherwise, if}\\&\text{the determinant is zero, the system of equation may have no}\\&\text{solution, or it may have an infinite number of them. To refresh,}\\&\text{to calculate a matrix of the given dimensions we use the formula:}\\&det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc\\&det\begin{bmatrix}6&-8\\3&12\end{bmatrix}=96\\&\text{There is a unique solution.}\end{align*}$

Report an Error

Example Question #111 : Linear Equations

$\begin{align*}&\text{Is there a unique solution for the equation }\\&\begin{bmatrix}0&-8&2\\-5&3&2\\20&12&-14\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}-163\\36\\22\end{bmatrix}?\end{align*}$

Possible Answers:

$\text{There is a unique solution.}$

$\text{There is not a unique solution.}$

Correct answer:

$\text{There is not a unique solution.}$

Explanation:

$\begin{align*}&\text{To determine whether or not the system of equations represented}\\&\text{by a matrix equation has a unique solution, one should calculate}\\&\text{the determinant. If the determinant is a nonzero value, then}\\&\text{the system of equations has a unique solution. Otherwise, if}\\&\text{the determinant is zero, the system of equation may have no}\\&\text{solution, or it may have an infinite number of them. To refresh,}\\&\text{to calculate a matrix of the given dimensions we use the formula:}\\&det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)\\&det\begin{bmatrix}0&-8&2\\-5&3&2\\20&12&-14\end{bmatrix}=0\\&\text{There is not a unique solution.}\end{align*}$

Report an Error

Example Question #1 : Criteria For Uniqueness And Consistency

$\begin{align*}&\text{Is there a unique solution for the equation }\\&\begin{bmatrix}13&13&-2\\12&12&12\\-16&-16&-11\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}28\\125\\107\end{bmatrix}?\end{align*}$

Possible Answers:

$\text{There is not a unique solution.}$

$\text{There is a unique solution.}$

Correct answer:

$\text{There is not a unique solution.}$

Explanation:

$\begin{align*}&\text{To determine whether or not the system of equations represented}\\&\text{by a matrix equation has a unique solution, one should calculate}\\&\text{the determinant. If the determinant is a nonzero value, then}\\&\text{the system of equations has a unique solution. Otherwise, if}\\&\text{the determinant is zero, the system of equation may have no}\\&\text{solution, or it may have an infinite number of them. To refresh,}\\&\text{to calculate a matrix of the given dimensions we use the formula:}\\&det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)\\&det\begin{bmatrix}13&13&-2\\12&12&12\\-16&-16&-11\end{bmatrix}=0\\&\text{There is not a unique solution.}\end{align*}$

Report an Error

Example Question #6 : Criteria For Uniqueness And Consistency

$\begin{align*}&\text{Decide if there is a unique solution for the equation: }\\&\begin{bmatrix}1&11&14\\-1&10&-12\\11&-5&16\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}59\\4\\-32\end{bmatrix}\end{align*}$

Possible Answers:

$\text{There is a unique solution.}$

$\text{There is not a unique solution.}$

Correct answer:

$\text{There is a unique solution.}$

Explanation:

$\begin{align*}&\text{To determine whether or not the system of equations represented}\\&\text{by a matrix equation has a unique solution, one should calculate}\\&\text{the determinant. If the determinant is a nonzero value, then}\\&\text{the system of equations has a unique solution. Otherwise, if}\\&\text{the determinant is zero, the system of equation may have no}\\&\text{solution, or it may have an infinite number of them. To refresh,}\\&\text{to calculate a matrix of the given dimensions we use the formula:}\\&det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)\\&det\begin{bmatrix}1&11&14\\-1&10&-12\\11&-5&16\end{bmatrix}=-2646\\&\text{There is a unique solution.}\end{align*}$

Report an Error

Example Question #1 : Criteria For Uniqueness And Consistency

$\begin{align*}&\text{Determine whether or not the equation }\\&\begin{bmatrix}9&-12\\-3&4\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-57\\182\end{bmatrix}\\&\text{has a unique solution.}\end{align*}$

Possible Answers:

$\text{There is a unique solution.}$

$\text{There is not a unique solution.}$

Correct answer:

$\text{There is not a unique solution.}$

Explanation:

$\begin{align*}&\text{To determine whether or not the system of equations represented}\\&\text{by a matrix equation has a unique solution, one should calculate}\\&\text{the determinant. If the determinant is a nonzero value, then}\\&\text{the system of equations has a unique solution. Otherwise, if}\\&\text{the determinant is zero, the system of equation may have no}\\&\text{solution, or it may have an infinite number of them. To refresh,}\\&\text{to calculate a matrix of the given dimensions we use the formula:}\\&det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc\\&det\begin{bmatrix}9&-12\\-3&4\end{bmatrix}=0\\&\text{There is not a unique solution.}\end{align*}$

Report an Error

Example Question #8 : Criteria For Uniqueness And Consistency

$\begin{align*}&\text{Determine whether or not the equation }\\&\begin{bmatrix}2&-5&-12\\8&7&1\\-10&-2&11\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}-71\\-38\\-50\end{bmatrix}\\&\text{has a unique solution.}\end{align*}$

Possible Answers:

$\text{There is a unique solution.}$

$\text{There is not a unique solution.}$

Correct answer:

$\text{There is not a unique solution.}$

Explanation:

$\begin{align*}&\text{To determine whether or not the system of equations represented}\\&\text{by a matrix equation has a unique solution, one should calculate}\\&\text{the determinant. If the determinant is a nonzero value, then}\\&\text{the system of equations has a unique solution. Otherwise, if}\\&\text{the determinant is zero, the system of equation may have no}\\&\text{solution, or it may have an infinite number of them. To refresh,}\\&\text{to calculate a matrix of the given dimensions we use the formula:}\\&det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)\\&det\begin{bmatrix}2&-5&-12\\8&7&1\\-10&-2&11\end{bmatrix}=0\\&\text{There is not a unique solution.}\end{align*}$

Report an Error

Example Question #2 : Criteria For Uniqueness And Consistency

$\begin{align*}&\text{Decide if there is a unique solution for the equation: }\\&\begin{bmatrix}19&-12\\9&18\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-126\\-163\end{bmatrix}\end{align*}$

Possible Answers:

$\text{There is a unique solution.}$

$\text{There is not a unique solution.}$

Correct answer:

$\text{There is a unique solution.}$

Explanation:

$\begin{align*}&\text{To determine whether or not the system of equations represented}\\&\text{by a matrix equation has a unique solution, one should calculate}\\&\text{the determinant. If the determinant is a nonzero value, then}\\&\text{the system of equations has a unique solution. Otherwise, if}\\&\text{the determinant is zero, the system of equation may have no}\\&\text{solution, or it may have an infinite number of them. To refresh,}\\&\text{to calculate a matrix of the given dimensions we use the formula:}\\&det\begin{vmatrix} a&b \\ c&d \end{vmatrix}=ad-bc\\&det\begin{bmatrix}19&-12\\9&18\end{bmatrix}=450\\&\text{There is a unique solution.}\end{align*}$

Report an Error

Example Question #10 : Criteria For Uniqueness And Consistency

$\begin{align*}&\text{Decide if there is a unique solution for the equation: }\\&\begin{bmatrix}3&-14&-20\\5&0&-3\\-6&8&14\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}125\\155\\-70\end{bmatrix}\end{align*}$

Possible Answers:

$\text{There is a unique solution.}$

$\text{There is not a unique solution.}$

Correct answer:

$\text{There is not a unique solution.}$

Explanation:

$\begin{align*}&\text{To determine whether or not the system of equations represented}\\&\text{by a matrix equation has a unique solution, one should calculate}\\&\text{the determinant. If the determinant is a nonzero value, then}\\&\text{the system of equations has a unique solution. Otherwise, if}\\&\text{the determinant is zero, the system of equation may have no}\\&\text{solution, or it may have an infinite number of them. To refresh,}\\&\text{to calculate a matrix of the given dimensions we use the formula:}\\&det\begin{vmatrix} a&b&c \\ d&e&f\\g&h&i \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)\\&det\begin{bmatrix}3&-14&-20\\5&0&-3\\-6&8&14\end{bmatrix}=0\\&\text{There is not a unique solution.}\end{align*}$

Report an Error

View Linear Algebra Tutors

Aarush
Certified Tutor

University of California, Berkeley, Bachelor, Electrical Engineering and Computer Science.

View Linear Algebra Tutors

Ping
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science. University of North Texas, Master of Arts, Education.

View Linear Algebra Tutors

Divyansh
Certified Tutor

Dalhousie University, Bachelor of Technology, Chemical Engineering.

All Linear Algebra Resources

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

Popular Subjects

GRE Tutors in Philadelphia, GMAT Tutors in Miami, GMAT Tutors in Houston, Computer Science Tutors in Seattle, Spanish Tutors in Phoenix, GMAT Tutors in Philadelphia, Computer Science Tutors in Philadelphia, LSAT Tutors in Miami, Calculus Tutors in Miami, Math Tutors in Phoenix

Popular Courses & Classes

SSAT Courses & Classes in Seattle, ACT Courses & Classes in New York City, SSAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Seattle, ACT Courses & Classes in Atlanta, LSAT Courses & Classes in Denver, SAT Courses & Classes in Houston, SAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Denver, GRE Courses & Classes in Chicago

Popular Test Prep

SAT Test Prep in Dallas Fort Worth, ACT Test Prep in Atlanta, SAT Test Prep in Boston, MCAT Test Prep in Houston, SAT Test Prep in New York City, SAT Test Prep in Philadelphia, ACT Test Prep in New York City, SSAT Test Prep in Philadelphia, ACT Test Prep in Houston, LSAT Test Prep in Miami

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 : Criteria for Uniqueness and Consistency

Study concepts, example questions & explanations for Linear Algebra

All Linear Algebra Resources

Example Questions

Example Question #1 : Criteria For Uniqueness And Consistency

Example Question #671 : Linear Algebra

Example Question #672 : Linear Algebra

Example Question #111 : Linear Equations

Example Question #1 : Criteria For Uniqueness And Consistency

Example Question #6 : Criteria For Uniqueness And Consistency

Example Question #1 : Criteria For Uniqueness And Consistency

Example Question #8 : Criteria For Uniqueness And Consistency

Example Question #2 : Criteria For Uniqueness And Consistency

Example Question #10 : Criteria For Uniqueness And Consistency

All Linear Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: