Call Now to Set Up Tutoring:

(888) 888-0446

Linear Algebra : 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 : Matrix Matrix Product

Compute $A\cdot B$ where,

$A=\begin{bmatrix} 3&4 &0 \\ 2&7 &1 \\ 6&5 &7 \end{bmatrix}$

$B =\begin{bmatrix} 2&2 &8 \\ 5&7 &0 \\ 6&4 &3 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 26&34 &24 \\ 45&57 &19 \\ 79&75 &69 \end{bmatrix}$

$\begin{bmatrix} 45&24 &10 \\ 45&57 &19 \\ 14&80 &70 \end{bmatrix}$

$\begin{bmatrix} 79&75 &69 \\ 45&57 &19 \\ 26&34 &24 \end{bmatrix}$

$\begin{bmatrix} 26&24 &34 \\ 45&57 &19 \\ 69&75 &71 \end{bmatrix}$

Not Possibe

Correct answer:

$\begin{bmatrix} 26&34 &24 \\ 45&57 &19 \\ 79&75 &69 \end{bmatrix}$

Explanation:

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together. To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix. For this example, our product matrix will have dimensions of (3x3). The product matrix equals, $\begin{bmatrix} (3\cdot 2+4\cdot 5+0\cdot 6)&(3\cdot 2 +4\cdot 7+0\cdot 4)&(3\cdot 8 +4\cdot 0+0\cdot 3) \\ (2\cdot 2 +7\cdot 5+1\cdot 6)&(2\cdot 2 +7\cdot 7+1\cdot 4)&(2\cdot 8 +7\cdot 0+1\cdot 3) \\ (6\cdot 2 +5\cdot 5+7\cdot 6)& (6\cdot 2 +5\cdot 7+7\cdot 4)&(7\cdot 8 +5\cdot 0+7\cdot 3) \end{bmatrix}$

Report an Error

Example Question #1 : Matrices

Compute $A\cdot B$ where,

$A=\begin{bmatrix} 4&5 &2 \end{bmatrix}$

$B=\begin{bmatrix} 0\\ 1 \\ 3 \end{bmatrix}$

Possible Answers:

Not Possible

$\begin{bmatrix} 4\\ 5 \\ 6 \end{bmatrix}$

$\begin{bmatrix} 4&6 & 5 \end{bmatrix}$

$\begin{bmatrix} 4&5 &6 \end{bmatrix}$

$\begin{bmatrix} 11 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 11 \end{bmatrix}$

Explanation:

Report an Error

Example Question #3 : Matrix Matrix Product

Compute $A\cdot B$ where,

$A=\begin{bmatrix} 4&5 & 6 \end{bmatrix}$

$B=\begin{bmatrix} 0&1 & 4 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 29 \end{bmatrix}$

$\begin{bmatrix} 0&5 & 24 \end{bmatrix}$

$\begin{bmatrix} 0\\ 5 \\ 24 \end{bmatrix}$

$\begin{bmatrix} 4& 8\\ 8&7 \end{bmatrix}$

Not Possible

Correct answer:

Not Possible

Explanation:

In order to be able to multiply matrices, the number of columns of the 1st matrix must equal the number of rows in the second matrix. Here, the first matrix has dimensions of (1x3). This means it has one row and three columns. The second matrix has dimensions of (1x3), also one row and three columns. Since $\tiny \tiny \small 3\neq1$ , we cannot multiply these two matrices together

Report an Error

Example Question #2 : Matrices

Compute $A\cdot B$ , where

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

$B = \begin{bmatrix} 2&2 \\ 5&7 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 34&26 \\ 53&39 \\ 47&37 \end{bmatrix}$

$\begin{bmatrix} 6&8 \\ 4&14 \\ 12&10 \end{bmatrix}$

Not Possible

$\begin{bmatrix} 26&34 \\ 39&53 \\ 37&47 \end{bmatrix}$

$\begin{bmatrix} -14&-22 \\ -31&-45 \\ -13&-23 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 26&34 \\ 39&53 \\ 37&47 \end{bmatrix}$

Explanation:

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together. To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix. For this example, our product matrix will have dimensions of (3x2). The product matrix equals, $\begin{bmatrix} (3\cdot 2+4\cdot 5)&(3\cdot 2 +4\cdot 7) \\ (2\cdot 2 +7\cdot 5)&(2\cdot 2 +7\cdot 7) \\ (6\cdot 2 +5\cdot 5)& (6\cdot 2 +5\cdot 7) \end{bmatrix}$

Report an Error

Example Question #5 : Matrix Matrix Product

Compute $A\cdot B$ where,

$A=\begin{bmatrix} 4& 5 \end{bmatrix}$

$B=\begin{bmatrix} 0& 4&2 \\ 7&0 &1 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 35\\ 16 \\ 13 \end{bmatrix}$

Not Possible

$\begin{bmatrix} 35&16 & 13 \end{bmatrix}$

$\begin{bmatrix} 0&35 \\ 16& 13 \end{bmatrix}$

$\begin{bmatrix} 13&16 & 35 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 35&16 & 13 \end{bmatrix}$

Explanation:

Report an Error

Example Question #6 : Matrix Matrix Product

Compute $A\cdot B$ where,

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

$B=\begin{bmatrix} 7\\ 5 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 5\\ 7 \end{bmatrix}$

$\begin{bmatrix} 12 \end{bmatrix}$

$\begin{bmatrix} 7\\ 5 \end{bmatrix}$

Not Possible

$\begin{bmatrix} 7&5 \\ 5& 7 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 5\\ 7 \end{bmatrix}$

Explanation:

Report an Error

Example Question #3 : Matrix Matrix Product

Compute $A\cdot B$ where,

$A=\begin{bmatrix} 1\\ 2\\ 5 \end{bmatrix}$

$B=\begin{bmatrix} 1\\ 5 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 2& 25 \end{bmatrix}$

$\begin{bmatrix} 2&25 \\ 7& 3 \end{bmatrix}$

$\begin{bmatrix} 1\\ 25 \end{bmatrix}$

Not Possible

$\begin{bmatrix} 2\\ 7 \\25 \end{bmatrix}$

Correct answer:

Not Possible

Explanation:

Since the number of columns in the first matrix does not equal the number of rows in the second matrix, you cannot multiply these two matrices.

Report an Error

Example Question #1 : Matrices

Compute $A\cdot B$ where,

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

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

Possible Answers:

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

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

Not Possible

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

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

Correct answer:

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

Explanation:

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together. To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix. For this example, our product matrix will have dimensions of (2x2). The product matrix equals, $\begin{bmatrix} (0\cdot 1+0\cdot 0)&(0\cdot 1 +0\cdot 0)\\(1\cdot 1 +1\cdot 0)&(1\cdot 1 +1\cdot 0) \end{bmatrix}$

Report an Error

Example Question #2 : Matrices

Compute $A\cdot B$ where,

$A=\begin{bmatrix} 12 \end{bmatrix}$

$B=\begin{bmatrix} 4&5 &1 &0 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 48\\ 60\\ 12\\ 0 \end{bmatrix}$

$\begin{bmatrix} 16&17 & 13& 12 \end{bmatrix}$

Not Possible

$\begin{bmatrix} 48& 60&12 & 0 \end{bmatrix}$

$\begin{bmatrix} 0\\ 12\\ 60\\ 48 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 48& 60&12 & 0 \end{bmatrix}$

Explanation:

Report an Error

Example Question #10 : Matrix Matrix Product

Compute $A\cdot B$ where,

$A=\begin{bmatrix} 0&1 &4 \\ 4&0 &7 \\ 2& 5& 0 \end{bmatrix}$

$B=\begin{bmatrix} 1\\ 2\\ 0 \end{bmatrix}$

Possible Answers:

Not Possible

$\begin{bmatrix} 2& 4&12 \end{bmatrix}$

$\begin{bmatrix} 0&1 &4 \\ 8&0 &14 \\ 0&0 &0 \end{bmatrix}$

$\begin{bmatrix} 2\\ 4\\ 12 \end{bmatrix}$

$\begin{bmatrix} 25 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 2\\ 4\\ 12 \end{bmatrix}$

Explanation:

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together. To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix. For this example, our product matrix will have dimensions of (3x1). The product matrix equals, $\begin{bmatrix} (0\cdot 1+1\cdot 2+4\cdot 0)\\(4\cdot 1+0\cdot 2+7\cdot 0)\\(2\cdot 1+5\cdot 2+0\cdot 0)\end{bmatrix}$

Report an Error

View Linear Algebra Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View Linear Algebra Tutors

Michael
Certified Tutor

Cleveland State University, Bachelor of Science, Mathematics.

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

Computer Science Tutors in Seattle, ISEE Tutors in Los Angeles, Computer Science Tutors in Washington DC, Calculus Tutors in Atlanta, Algebra Tutors in Atlanta, Calculus Tutors in San Francisco-Bay Area, GRE Tutors in Philadelphia, MCAT Tutors in Washington DC, SAT Tutors in Atlanta, Physics Tutors in San Diego

Popular Courses & Classes

GRE Courses & Classes in New York City, GMAT Courses & Classes in Miami, GMAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Los Angeles, MCAT Courses & Classes in San Diego, GRE Courses & Classes in Miami, ISEE Courses & Classes in Houston, ISEE Courses & Classes in Denver, MCAT Courses & Classes in Washington DC, MCAT Courses & Classes in Atlanta

Popular Test Prep

LSAT Test Prep in Boston, GRE Test Prep in Dallas Fort Worth, SSAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Seattle, GRE Test Prep in Miami, GMAT Test Prep in Miami, SSAT Test Prep in Houston, ISEE Test Prep in Miami, MCAT Test Prep in Denver, ISEE Test Prep in Phoenix

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 : Matrices

Study concepts, example questions & explanations for Linear Algebra

All Linear Algebra Resources

Example Questions

Example Question #1 : Matrix Matrix Product

Example Question #1 : Matrices

Example Question #3 : Matrix Matrix Product

Example Question #2 : Matrices

Example Question #5 : Matrix Matrix Product

Example Question #6 : Matrix Matrix Product

Example Question #3 : Matrix Matrix Product

Example Question #1 : Matrices

Example Question #2 : Matrices

Example Question #10 : Matrix Matrix Product

All Linear Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: