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:

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

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

Correct answer:

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

Explanation:

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

Report an Error

Example Question #1 : Criteria For Uniqueness And Consistency

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

Possible Answers:

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

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

Correct answer:

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

Explanation:

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

Report an Error

Example Question #2 : Criteria For Uniqueness And Consistency

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

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 #4 : Criteria For Uniqueness And Consistency

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

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 #5 : 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:

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

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

Correct answer:

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

Explanation:

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

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 #4 : 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:

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

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

Correct answer:

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

Explanation:

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

Report an Error

Example Question #4 : 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 #9 : 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

Steven
Certified Tutor

University of Puerto Rico, Bachelor of Science, Mathematics. Nova Southeastern University, Master of Arts, Mathematics Teache...

View Linear Algebra Tutors

Christopher
Certified Tutor

University of Michigan-Ann Arbor, Bachelor of Science, Computer Science.

View Linear Algebra Tutors

Mohammed
Certified Tutor

Institute of Business Administration - Pakistan, Bachelor of Economics, Economics.

All Linear Algebra Resources

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

Popular Subjects

English Tutors in Miami, Spanish Tutors in San Francisco-Bay Area, English Tutors in Chicago, SSAT Tutors in Miami, Chemistry Tutors in Seattle, Reading Tutors in Dallas Fort Worth, Calculus Tutors in Phoenix, Biology Tutors in Phoenix, ACT Tutors in Boston, ISEE Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Chicago, GMAT Courses & Classes in Chicago, MCAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Denver, ACT Courses & Classes in Miami, SSAT Courses & Classes in San Diego, ACT Courses & Classes in Philadelphia, GMAT Courses & Classes in Atlanta, SAT Courses & Classes in Atlanta

Popular Test Prep

ACT Test Prep in Boston, GMAT Test Prep in Atlanta, SSAT Test Prep in Boston, LSAT Test Prep in Atlanta, SAT Test Prep in Washington DC, ACT Test Prep in Miami, SAT Test Prep in Dallas Fort Worth, GRE Test Prep in Chicago, ACT Test Prep in Philadelphia, ISEE Test Prep in Washington DC

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 #1 : Criteria For Uniqueness And Consistency

Example Question #2 : Criteria For Uniqueness And Consistency

Example Question #4 : Criteria For Uniqueness And Consistency

Example Question #5 : Criteria For Uniqueness And Consistency

Example Question #6 : Criteria For Uniqueness And Consistency

Example Question #1 : Criteria For Uniqueness And Consistency

Example Question #4 : Criteria For Uniqueness And Consistency

Example Question #4 : Criteria For Uniqueness And Consistency

Example Question #9 : 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: