Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Find the Product of Two Matrices

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #572 : Pre Calculus

Calculate AB when

$A=\begin{bmatrix}-1 & 3\\0 & 3\\2 &1 \end{bmatrix}$ $\displaystyle A=\begin{bmatrix}-1 & 3\\0 & 3\\2 &1 \end{bmatrix}$ and $B=\begin{bmatrix} -2& 4\\ 3&1 \end{bmatrix}$ $\displaystyle B=\begin{bmatrix} -2& 4\\ 3&1 \end{bmatrix}$ .

Possible Answers:

$AB=\begin{bmatrix} 9&-5 \\ -3&0 \\ -6&4 \end{bmatrix}$ $\displaystyle AB=\begin{bmatrix} 9&-5 \\ -3&0 \\ -6&4 \end{bmatrix}$

$AB=\begin{bmatrix} 11& -1\\ 9& 3\\ -1&9 \end{bmatrix}$ $\displaystyle AB=\begin{bmatrix} 11& -1\\ 9& 3\\ -1&9 \end{bmatrix}$

$AB=\begin{bmatrix} 3&-2 \\ 5&0 \end{bmatrix}$ $\displaystyle AB=\begin{bmatrix} 3&-2 \\ 5&0 \end{bmatrix}$

$AB=\begin{bmatrix} 6& -7\\ 5& 12\\ -1&3 \end{bmatrix}$ $\displaystyle AB=\begin{bmatrix} 6& -7\\ 5& 12\\ -1&3 \end{bmatrix}$

$AB=\begin{bmatrix} 4&3 \\ -2&4 \end{bmatrix}$ $\displaystyle AB=\begin{bmatrix} 4&3 \\ -2&4 \end{bmatrix}$

Correct answer:

$AB=\begin{bmatrix} 11& -1\\ 9& 3\\ -1&9 \end{bmatrix}$ $\displaystyle AB=\begin{bmatrix} 11& -1\\ 9& 3\\ -1&9 \end{bmatrix}$

Explanation:

In order to perform matrix multiplication, the number of columns in the first matrix has to be the same as the number of rows in the second column.

$A:3x2\:\, B:2x2$ $\displaystyle A:3x2\:\, B:2x2$

$AB=\begin{bmatrix}-1 & 3\\0 & 3\\2 &1 \end{bmatrix}\cdot \begin{bmatrix} -2&4 \\ 3&1 \end{bmatrix}$ $\displaystyle AB=\begin{bmatrix}-1 & 3\\0 & 3\\2 &1 \end{bmatrix}\cdot \begin{bmatrix} -2&4 \\ 3&1 \end{bmatrix}$

From here, we multiply each term in the first matrix's row by the first column in the second matrix. Continue in this fashion to get the product matrix.

$AB=\begin{bmatrix} (-1)(-2)+(3)(3)& (-1)(4)+(3)(1)\\ (0)(-2)+(3)(3)&(0)(4)+(3)(1) \\ (2)(-2)+(1)(3)&(2)(4)+(1)(1) \end{bmatrix}$ $\displaystyle AB=\begin{bmatrix} (-1)(-2)+(3)(3)& (-1)(4)+(3)(1)\\ (0)(-2)+(3)(3)&(0)(4)+(3)(1) \\ (2)(-2)+(1)(3)&(2)(4)+(1)(1) \end{bmatrix}$

$AB=\begin{bmatrix} 11& -1\\ 9& 3\\ -1&9 \end{bmatrix}$ $\displaystyle AB=\begin{bmatrix} 11& -1\\ 9& 3\\ -1&9 \end{bmatrix}$

Report an Error

Example Question #68 : Matrices And Vectors

Evaluate: $\begin{bmatrix} 2&7 \\ 6&-5 \end{bmatrix} \begin{bmatrix} 3& 4\\ 2&1 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 2&7 \\ 6&-5 \end{bmatrix} \begin{bmatrix} 3& 4\\ 2&1 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 25&30 \\ -3&-4\end{bmatrix}$ $\displaystyle \begin{bmatrix} 25&30 \\ -3&-4\end{bmatrix}$

$\begin{bmatrix} 20&15 \\ 8&19 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 20&15 \\ 8&19 \end{bmatrix}$

$\begin{bmatrix}34&11 \\ -2&7 \end{bmatrix}$ $\displaystyle \begin{bmatrix}34&11 \\ -2&7 \end{bmatrix}$

$\begin{bmatrix}11&34 \\ 7&-2 \end{bmatrix}$ $\displaystyle \begin{bmatrix}11&34 \\ 7&-2 \end{bmatrix}$

$\begin{bmatrix} 6&28 \\ 12&-5 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 6&28 \\ 12&-5 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 20&15 \\ 8&19 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 20&15 \\ 8&19 \end{bmatrix}$

Explanation:

Write the rule for multiplying a two by two matrix. The result will be a two by two matrix.

$\begin{bmatrix} a& b\\ c&d\end{bmatrix} \begin{bmatrix} w&x \\ y&z \end{bmatrix} = \begin{bmatrix} aw+by&ax+bz \\ cw+dy&cx+dz \end{bmatrix}$ $\displaystyle \begin{bmatrix} a& b\\ c&d\end{bmatrix} \begin{bmatrix} w&x \\ y&z \end{bmatrix} = \begin{bmatrix} aw+by&ax+bz \\ cw+dy&cx+dz \end{bmatrix}$

Follow this rule for the given problem.

$\begin{bmatrix} 2&7 \\ 6&-5 \end{bmatrix} \begin{bmatrix} 3& 4\\ 2&1 \end{bmatrix}= \begin{bmatrix} (2)(3)+(7)(2)&(2)(4)+(7)(1) \\ (6)(3)+(-5)(2)&(6)(4)+(-5)(1) \end{bmatrix}$ $\displaystyle \begin{bmatrix} 2&7 \\ 6&-5 \end{bmatrix} \begin{bmatrix} 3& 4\\ 2&1 \end{bmatrix}= \begin{bmatrix} (2)(3)+(7)(2)&(2)(4)+(7)(1) \\ (6)(3)+(-5)(2)&(6)(4)+(-5)(1) \end{bmatrix}$

Simplify, and the answer is: $\begin{bmatrix} 20&15 \\ 8&19 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 20&15 \\ 8&19 \end{bmatrix}$

Report an Error

Example Question #31 : Multiplication Of Matrices

Multiply the matrices: $\begin{bmatrix} 1& 3 \end{bmatrix}\begin{bmatrix} 4&9 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 1& 3 \end{bmatrix}\begin{bmatrix} 4&9 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 5& 12 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 5& 12 \end{bmatrix}$

$\textup{Cannot be solved.}$

$\begin{bmatrix} 4& 27 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4& 27 \end{bmatrix}$

108 $\displaystyle 108$

$\displaystyle 31$

Correct answer:

$\textup{Cannot be solved.}$

Explanation:

In order to multiply these matrices we will need to consider the rows and columns for each matrix.

Both matrices have a dimension of $1\times 2$ $\displaystyle 1\times 2$ .

The rule for multiplying matrices is where the number of columns of the first matrix must match the number of rows of the second matrix.

If the dimensions of the first matrix are $a\times b$ $\displaystyle a\times b$ , and the dimensions of the second matrix are $b\times c$ $\displaystyle b\times c$ , then we will get a dimension of $a \times c$ $\displaystyle a \times c$ matrix as a result. If the value of $\displaystyle b$ are not matched, we cannot evaluate the product of the matrices.

The correct answer is: $\textup{Cannot be solved.}$

Report an Error

Example Question #61 : Matrices And Vectors

Find the product of A and B.

$A=\begin{bmatrix} 3 &-1 &4 \end{bmatrix}$ $\displaystyle A=\begin{bmatrix} 3 &-1 &4 \end{bmatrix}$

$B=\begin{bmatrix} 2\\ 1\\-3 \end{bmatrix}$ $\displaystyle B=\begin{bmatrix} 2\\ 1\\-3 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -7 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -7 \end{bmatrix}$

$\begin{bmatrix} 6 & -2& -1\\4 &3 &-6 \\2 &5 &6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 6 & -2& -1\\4 &3 &-6 \\2 &5 &6 \end{bmatrix}$

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

$\begin{bmatrix} 6 &-1 &-12 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 6 &-1 &-12 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -7 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -7 \end{bmatrix}$

Explanation:

Since you are multiplying a $1\times 3$ $\displaystyle 1\times 3$ to a $3\times 1$ $\displaystyle 3\times 1$ , the answer is going to be a $1\times 1$ $\displaystyle 1\times 1$ .

To solve, simply multiply each corresponding element and add together.

Thus, your answer is

[-7] $\displaystyle [-7]$ .

Report an Error

View Pre-Calculus Tutors

Zina
Certified Tutor

Oakland University, Bachelor in Arts, English.

View Pre-Calculus Tutors

Anjali
Certified Tutor

Delhi University, Bachelor of Science, Physics. Kumuan University, Master of Science, Physics.

View Pre-Calculus Tutors

Andrew
Certified Tutor

Northern Arizona University, Bachelor of Philosophy, Philosophy.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in San Francisco-Bay Area, Computer Science Tutors in Denver, Spanish Tutors in Dallas Fort Worth, SAT Tutors in Phoenix, LSAT Tutors in Miami, Statistics Tutors in San Diego, ISEE Tutors in Atlanta, French Tutors in Houston, Algebra Tutors in Boston, LSAT Tutors in Seattle

Popular Courses & Classes

GRE Courses & Classes in Atlanta, LSAT Courses & Classes in Denver, MCAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Boston, SAT Courses & Classes in Phoenix, ISEE Courses & Classes in San Diego, Spanish Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Denver, Spanish Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Atlanta, ACT Test Prep in Atlanta, ISEE Test Prep in Dallas Fort Worth, SAT Test Prep in Philadelphia, SAT Test Prep in Chicago, SAT Test Prep in Dallas Fort Worth, ACT Test Prep in Miami, MCAT Test Prep in Denver, MCAT Test Prep in Miami, MCAT Test Prep in Boston

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

Precalculus : Find the Product of Two Matrices

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #572 : Pre Calculus

Example Question #68 : Matrices And Vectors

Example Question #31 : Multiplication Of Matrices

Example Question #61 : Matrices And Vectors

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: