\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) \( \newcommand{\cm}{\mathrm{cm} } \) \( \newcommand{\sec}{ \, \mathrm{sec} \, } \) \( \newcommand{\vhat}[1]{\,\hat{#1}} \) \( \newcommand{\vhati}{\,\hat{i}} \) \( \newcommand{\vhatj}{\,\hat{j}} \) \( \newcommand{\vhatk}{\,\hat{k}} \) \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) \( \newcommand{\norm}[1]{\|{#1}\|} \) \( \newcommand{\arccot}{ \, \mathrm{arccot} \, } \) \( \newcommand{\arcsec}{ \, \mathrm{arcsec} \, } \) \( \newcommand{\arccsc}{ \, \mathrm{arccsc} \, } \) \( \newcommand{\sech}{ \, \mathrm{sech} \, } \) \( \newcommand{\csch}{ \, \mathrm{csch} \, } \) \( \newcommand{\arcsinh}{ \, \mathrm{arcsinh} \, } \) \( \newcommand{\arccosh}{ \, \mathrm{arccosh} \, } \) \( \newcommand{\arctanh}{ \, \mathrm{arctanh} \, } \) \( \newcommand{\arccoth}{ \, \mathrm{arccoth} \, } \) \( \newcommand{\arcsech}{ \, \mathrm{arcsech} \, } \) \( \newcommand{\arccsch}{ \, \mathrm{arccsch} \, } \)

17Calculus Precalculus - Matrix Multiplication

Algebra

Polynomials

Functions

Rational Functions

Graphing

Matrices

Systems

Trigonometry

Complex Numbers

Applications

Practice

Practice Problems

Practice Exams

Tools

Articles

Algebra

Functions

Functions

Polynomials

Rational Functions

Graphing

Matrices & Systems

Matrices

Systems

Trigonometry & Complex Numbers

Trigonometry

Complex Numbers

Applications

SV Calculus

MV Calculus

Practice

Practice Problems

Practice Exams

Tools

Articles

As discussed on the basics of matrices page, multiplying two matrices together is not as simple as multiplying two numbers together. Here is a good introduction video and example. He explains quite thoroughly how to do matrix multiplication.

Khan Academy - Matrix multiplication introduction [6min-25secs]

video by Khan Academy

Let's work a few practice problems.

Unless otherwise instructed, perform matrix multiplication on these matrices.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\left[\begin{array}{rr} 1 & 2 \\ 3 & 4 \end{array}\right] \left[\begin{array}{rr} 5 & 6 \\ 7 & 8 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\left[\begin{array}{rr} 1 & 2 \\ 3 & 4 \end{array}\right] \left[\begin{array}{rr} 5 & 6 \\ 7 & 8 \end{array}\right] \)

Final Answer

\(\left[\begin{array}{rr} 19 & 22 \\ 43 & 50 \end{array}\right]\)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\left[\begin{array}{rr} 1 & 2 \\ 3 & 4 \end{array}\right] \left[\begin{array}{rr} 5 & 6 \\ 7 & 8 \end{array}\right] \)

Solution

2015 video

video by PatrickJMT

Final Answer

\(\left[\begin{array}{rr} 19 & 22 \\ 43 & 50 \end{array}\right]\)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{ \left[\begin{array}{rr} 2 & 1 \\ 3 & 4 \\ 5 & 6 \end{array}\right] \left[\begin{array}{rrr} 1 & 3 & 6 \\ 2 & 4 & 5 \end{array}\right] }\)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{ \left[\begin{array}{rr} 2 & 1 \\ 3 & 4 \\ 5 & 6 \end{array}\right] \left[\begin{array}{rrr} 1 & 3 & 6 \\ 2 & 4 & 5 \end{array}\right] }\)

Final Answer

\(\displaystyle{\left[\begin{array}{rrr} 4 & 10 & 17 \\ 11 & 25 & 38 \\ 17 & 39 & 60\end{array}\right]}\)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{ \left[\begin{array}{rr} 2 & 1 \\ 3 & 4 \\ 5 & 6 \end{array}\right] \left[\begin{array}{rrr} 1 & 3 & 6 \\ 2 & 4 & 5 \end{array}\right] }\)

Solution

2016 video

video by PatrickJMT

Final Answer

\(\displaystyle{\left[\begin{array}{rrr} 4 & 10 & 17 \\ 11 & 25 & 38 \\ 17 & 39 & 60\end{array}\right]}\)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{ \left[\begin{array}{rrr} 1 & 2 & 3 \\ 0 & -1 & 5\end{array}\right] \left[\begin{array}{r} 1 \\ 2 \\ -4\end{array}\right] }\)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{ \left[\begin{array}{rrr} 1 & 2 & 3 \\ 0 & -1 & 5\end{array}\right] \left[\begin{array}{r} 1 \\ 2 \\ -4\end{array}\right] }\)

Final Answer

\(\displaystyle{\left[\begin{array}{r}-7 \\ -22\end{array}\right]}\)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{ \left[\begin{array}{rrr} 1 & 2 & 3 \\ 0 & -1 & 5\end{array}\right] \left[\begin{array}{r} 1 \\ 2 \\ -4\end{array}\right] }\)

Solution

2018 video

video by PatrickJMT

Final Answer

\(\displaystyle{\left[\begin{array}{r}-7 \\ -22\end{array}\right]}\)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{\left[\begin{array}{rrr} 4 & 1 & 3 \\ 2 & -5 & 7\end{array}\right] \left[\begin{array}{rr} -2 & 3 \\ -4 & -2 \\ 5 & 1 \end{array}\right] }\)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{\left[\begin{array}{rrr} 4 & 1 & 3 \\ 2 & -5 & 7\end{array}\right] \left[\begin{array}{rr} -2 & 3 \\ -4 & -2 \\ 5 & 1 \end{array}\right] }\)

Final Answer

\(\displaystyle{\left[\begin{array}{rr} 3 & 13 \\ 51 & 23\end{array}\right]}\)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{\left[\begin{array}{rrr} 4 & 1 & 3 \\ 2 & -5 & 7\end{array}\right] \left[\begin{array}{rr} -2 & 3 \\ -4 & -2 \\ 5 & 1 \end{array}\right] }\)

Solution

2019 video

video by MIP4U

Final Answer

\(\displaystyle{\left[\begin{array}{rr} 3 & 13 \\ 51 & 23\end{array}\right]}\)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{\left[\begin{array}{rr} -2 & 3 \\ -4 & -2 \\ 5 & 1 \end{array}\right] \left[\begin{array}{rrr} 4 & 1 & 3 \\ 2 & -5 & 7\end{array}\right] }\)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{\left[\begin{array}{rr} -2 & 3 \\ -4 & -2 \\ 5 & 1 \end{array}\right] \left[\begin{array}{rrr} 4 & 1 & 3 \\ 2 & -5 & 7\end{array}\right] }\)

Final Answer

\(\displaystyle{\left[\begin{array}{rrr} -2 & -17 & 15 \\ -20 & 6 & -26 \\ 22 & 0 & 22\end{array}\right]}\)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\(\displaystyle{\left[\begin{array}{rr} -2 & 3 \\ -4 & -2 \\ 5 & 1 \end{array}\right] \left[\begin{array}{rrr} 4 & 1 & 3 \\ 2 & -5 & 7\end{array}\right] }\)

Solution

2020 video

video by MIP4U

Final Answer

\(\displaystyle{\left[\begin{array}{rrr} -2 & -17 & 15 \\ -20 & 6 & -26 \\ 22 & 0 & 22\end{array}\right]}\)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( A = \left[\begin{array}{rrr} 3 & 1 & 4 \end{array}\right] \)
\( B = \left[\begin{array}{rr} 4 & 3 \\ 2 & 5 \\ 6 & 8 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( A = \left[\begin{array}{rrr} 3 & 1 & 4 \end{array}\right] \)
\( B = \left[\begin{array}{rr} 4 & 3 \\ 2 & 5 \\ 6 & 8 \end{array}\right] \)

Final Answer

\( A \cdot B = \left[\begin{array}{rr} 38 & 46 \end{array} \right] \)
\( B \cdot A \) does not make sense.

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( A = \left[\begin{array}{rrr} 3 & 1 & 4 \end{array}\right] \)
\( B = \left[\begin{array}{rr} 4 & 3 \\ 2 & 5 \\ 6 & 8 \end{array}\right] \)

Solution

2877 video

Final Answer

\( A \cdot B = \left[\begin{array}{rr} 38 & 46 \end{array} \right] \)
\( B \cdot A \) does not make sense.

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, calculate \( A \cdot B \) using these matrices.
\( A = \left[\begin{array}{rr} 3 & 4 \\ 7 & 2 \\ 5 & 9 \end{array}\right] \)
\( B = \left[\begin{array}{rrr} 3 & 1 & 5 \\ 6 & 9 & 7 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, calculate \( A \cdot B \) using these matrices.
\( A = \left[\begin{array}{rr} 3 & 4 \\ 7 & 2 \\ 5 & 9 \end{array}\right] \)
\( B = \left[\begin{array}{rrr} 3 & 1 & 5 \\ 6 & 9 & 7 \end{array}\right] \)

Final Answer

\( A \cdot B = \left[\begin{array}{rrr} 33 & 39 & 43 \\ 33 & 25 & 49 \\ 69 & 86 & 88 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, calculate \( A \cdot B \) using these matrices.
\( A = \left[\begin{array}{rr} 3 & 4 \\ 7 & 2 \\ 5 & 9 \end{array}\right] \)
\( B = \left[\begin{array}{rrr} 3 & 1 & 5 \\ 6 & 9 & 7 \end{array}\right] \)

Solution

2878 video

Final Answer

\( A \cdot B = \left[\begin{array}{rrr} 33 & 39 & 43 \\ 33 & 25 & 49 \\ 69 & 86 & 88 \end{array}\right] \)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( A = \left[ \begin{array}{rrr} 2 & 5 & 6 \end{array} \right] \)
\( B = \left[\begin{array}{r} 3 \\ 4 \\ -5 \end{array} \right]\)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( A = \left[ \begin{array}{rrr} 2 & 5 & 6 \end{array} \right] \)
\( B = \left[\begin{array}{r} 3 \\ 4 \\ -5 \end{array} \right]\)

Final Answer

\( AB = [ -4 ] \)
\( BA = \left[\begin{array}{rrr} 6 & 15 & 18 \\ 8 & 20 & 24 \\ -10 & -25 & -30 \end{array} \right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( A = \left[ \begin{array}{rrr} 2 & 5 & 6 \end{array} \right] \)
\( B = \left[\begin{array}{r} 3 \\ 4 \\ -5 \end{array} \right]\)

Solution

2879 video

Final Answer

\( AB = [ -4 ] \)
\( BA = \left[\begin{array}{rrr} 6 & 15 & 18 \\ 8 & 20 & 24 \\ -10 & -25 & -30 \end{array} \right] \)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( A = \left[\begin{array}{rrr} 1 & 4 & -2 \\ 3 & 5 & -6 \end{array}\right] \)
\( B = \left[\begin{array}{rrrr} 5 & 2 & 8 & -1 \\ 3 & 6 & 4 & 5 \\ -2 & 9 & 7 & -3 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( A = \left[\begin{array}{rrr} 1 & 4 & -2 \\ 3 & 5 & -6 \end{array}\right] \)
\( B = \left[\begin{array}{rrrr} 5 & 2 & 8 & -1 \\ 3 & 6 & 4 & 5 \\ -2 & 9 & 7 & -3 \end{array}\right] \)

Final Answer

\( AB = \left[\begin{array}{rrrr} 21 & 8 & 10 & 25 \\ 42 & -18 & 2 & 40 \end{array} \right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( A = \left[\begin{array}{rrr} 1 & 4 & -2 \\ 3 & 5 & -6 \end{array}\right] \)
\( B = \left[\begin{array}{rrrr} 5 & 2 & 8 & -1 \\ 3 & 6 & 4 & 5 \\ -2 & 9 & 7 & -3 \end{array}\right] \)

Solution

2880 video

Final Answer

\( AB = \left[\begin{array}{rrrr} 21 & 8 & 10 & 25 \\ 42 & -18 & 2 & 40 \end{array} \right] \)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rrr} 2 & 1 & 3 \\ 0 & -1 & 4 \end{array}\right] \) \( \left[\begin{array}{r} 1 \\ 0 \\ 5 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rrr} 2 & 1 & 3 \\ 0 & -1 & 4 \end{array}\right] \) \( \left[\begin{array}{r} 1 \\ 0 \\ 5 \end{array}\right] \)

Final Answer

\( \left[\begin{array}{r} 17 \\ 20 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rrr} 2 & 1 & 3 \\ 0 & -1 & 4 \end{array}\right] \) \( \left[\begin{array}{r} 1 \\ 0 \\ 5 \end{array}\right] \)

Solution

2881 video

Final Answer

\( \left[\begin{array}{r} 17 \\ 20 \end{array}\right] \)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rr} 1 & 7 \\ -2 & 0 \end{array}\right] \) \( \left[\begin{array}{rr} 5 & 1 \\ 3 & 2 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rr} 1 & 7 \\ -2 & 0 \end{array}\right] \) \( \left[\begin{array}{rr} 5 & 1 \\ 3 & 2 \end{array}\right] \)

Final Answer

\( \left[\begin{array}{rr} 26 & 15 \\ -10 & -2 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rr} 1 & 7 \\ -2 & 0 \end{array}\right] \) \( \left[\begin{array}{rr} 5 & 1 \\ 3 & 2 \end{array}\right] \)

Solution

2882 video

Final Answer

\( \left[\begin{array}{rr} 26 & 15 \\ -10 & -2 \end{array}\right] \)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rr} 1 & 2 \end{array}\right] \) \( \left[\begin{array}{rr} 3 & -1 \\ 0 & 2 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rr} 1 & 2 \end{array}\right] \) \( \left[\begin{array}{rr} 3 & -1 \\ 0 & 2 \end{array}\right] \)

Final Answer

\( \left[\begin{array}{rr} 3 & 3 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rr} 1 & 2 \end{array}\right] \) \( \left[\begin{array}{rr} 3 & -1 \\ 0 & 2 \end{array}\right] \)

Solution

2883 video

Final Answer

\( \left[\begin{array}{rr} 3 & 3 \end{array}\right] \)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rrr} 2 & 1 & 0 \\ 3 & 0 & -1 \end{array}\right] \) \( \left[\begin{array}{rr} 1 & 4 \\ 0 & 2 \\ 5 & 1 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rrr} 2 & 1 & 0 \\ 3 & 0 & -1 \end{array}\right] \) \( \left[\begin{array}{rr} 1 & 4 \\ 0 & 2 \\ 5 & 1 \end{array}\right] \)

Final Answer

\( \left[\begin{array}{rr} 2 & 10 \\ -2 & 11 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rrr} 2 & 1 & 0 \\ 3 & 0 & -1 \end{array}\right] \) \( \left[\begin{array}{rr} 1 & 4 \\ 0 & 2 \\ 5 & 1 \end{array}\right] \)

Solution

2884 video

Final Answer

\( \left[\begin{array}{rr} 2 & 10 \\ -2 & 11 \end{array}\right] \)

close solution

Log in to rate this practice problem and to see it's current rating.

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rrr} -2 & 3 & 4 \\ 4 & 0 & 1 \end{array}\right] \) \( \left[\begin{array}{rrrr} 0 & -3 & 4 & -1 \\ 1 & 3 & 0 & -5 \\ -4 & 4 & 3 & -2 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rrr} -2 & 3 & 4 \\ 4 & 0 & 1 \end{array}\right] \) \( \left[\begin{array}{rrrr} 0 & -3 & 4 & -1 \\ 1 & 3 & 0 & -5 \\ -4 & 4 & 3 & -2 \end{array}\right] \)

Final Answer

\( \left[\begin{array}{rrrr} 19 & -1 & -20 & -5 \\ 4 & -16 & 13 & -2 \end{array}\right] \)

Problem Statement

Unless otherwise instructed, perform matrix multiplication on these matrices.
\( \left[\begin{array}{rrr} -2 & 3 & 4 \\ 4 & 0 & 1 \end{array}\right] \) \( \left[\begin{array}{rrrr} 0 & -3 & 4 & -1 \\ 1 & 3 & 0 & -5 \\ -4 & 4 & 3 & -2 \end{array}\right] \)

Solution

2885 video

Final Answer

\( \left[\begin{array}{rrrr} 19 & -1 & -20 & -5 \\ 4 & -16 & 13 & -2 \end{array}\right] \)

close solution

Log in to rate this practice problem and to see it's current rating.

matrix multiplication 17calculus youtube playlist

Really UNDERSTAND Precalculus

Topics You Need To Understand For This Page

To bookmark this page and practice problems, log in to your account or set up a free account.

Topics Listed Alphabetically

Single Variable Calculus

Multi-Variable Calculus

Differential Equations

Precalculus

Search Practice Problems

Do you have a practice problem number but do not know on which page it is found? If so, enter the number below and click 'page' to go to the page on which it is found or click 'practice' to be taken to the practice problem.

learning and study techniques

Get great tutoring at an affordable price with Chegg. Subscribe today and get your 1st 30 minutes Free!

The 17Calculus and 17Precalculus iOS and Android apps are no longer available for download. If you are still using a previously downloaded app, your app will be available until the end of 2020, after which the information may no longer be available. However, do not despair. All the information (and more) is now available on 17calculus.com for free.

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes

Shop eBags.com, the leading online retailer of luggage, handbags, backpacks, accessories, and more!

Prime Student 6-month Trial

How to Ace the Rest of Calculus: The Streetwise Guide, Including MultiVariable Calculus

Shop eBags.com, the leading online retailer of luggage, handbags, backpacks, accessories, and more!

Shop Amazon - Wearable Technology: Electronics

Do NOT follow this link or you will be banned from the site!

When using the material on this site, check with your instructor to see what they require. Their requirements come first, so make sure your notation and work follow their specifications.

DISCLAIMER - 17Calculus owners and contributors are not responsible for how the material, videos, practice problems, exams, links or anything on this site are used or how they affect the grades or projects of any individual or organization. We have worked, to the best of our ability, to ensure accurate and correct information on each page and solutions to practice problems and exams. However, we do not guarantee 100% accuracy. It is each individual's responsibility to verify correctness and to determine what different instructors and organizations expect. How each person chooses to use the material on this site is up to that person as well as the responsibility for how it impacts grades, projects and understanding of calculus, math or any other subject. In short, use this site wisely by questioning and verifying everything. If you see something that is incorrect, contact us right away so that we can correct it.

Links and banners on this page are affiliate links. We carefully choose only the affiliates that we think will help you learn. Clicking on them and making purchases help you support 17Calculus at no extra charge to you. However, only you can decide what will actually help you learn. So think carefully about what you need and purchase only what you think will help you.

We use cookies on this site to enhance your learning experience.

17calculus

Copyright © 2010-2020 17Calculus, All Rights Reserved     [Privacy Policy]     [Support]     [About]

mathjax.org
Real Time Web Analytics
17Calculus
We use cookies to ensure that we give you the best experience on our website. By using this site, you agree to our Website Privacy Policy.