We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Find the Sum or Difference 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 #1 : Find The Sum Or Difference Of Two Matrices

Subtract:

$\begin{bmatrix} 2& 6\\ 5& 3 \end{bmatrix}-\begin{bmatrix} 1& 7 \\ 9& 2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 1& -3\\ -2& 1 \end{bmatrix}$

$\begin{bmatrix} 1& -1\\ -4& 1 \end{bmatrix}$

$\begin{bmatrix} 0\\ -3 \end{bmatrix}$

$\begin{bmatrix} 52& 2\\ -22& 29 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 1& -1\\ -4& 1 \end{bmatrix}$

Explanation:

In order to subtract matrices, they have to be of the same dimension. In this case, they are both 2x2.

The formula to subtract matrices is as follows:

$\begin{bmatrix} a& b\\ c& d \end{bmatrix}-\begin{bmatrix} e& f\\ g& h \end{bmatrix}=\begin{bmatrix} a-e& b-f\\ c-g& d-h \end{bmatrix}$

Using this formula we plug in our values and solve:

Report an Error

Example Question #2 : Find The Sum Or Difference Of Two Matrices

Subtract:

$\begin{bmatrix} 3& 8\\ 10& 12 \end{bmatrix}$ $-\begin{bmatrix} 11\\ 9 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -61\\ -42 \end{bmatrix}$

$\begin{bmatrix} -33& -72\\ -110& -108 \end{bmatrix}$

No Solution

$\begin{bmatrix} -39\\ 2 \end{bmatrix}$

Correct answer:

No Solution

Explanation:

In order to subtract matrices, they have to be of the same dimension. In this case, they are not. One is 2x2 while the other is 2x1.

As such, we cannot find their difference.

The answer is No Solution.

Report an Error

Example Question #3 : Find The Sum Or Difference Of Two Matrices

Subtract

$\begin{bmatrix} 10& 5\\ 7& 3 \end{bmatrix}-$ $2\begin{bmatrix} 1& 0\\ 5& 2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -8& 5\\ 3& -7 \end{bmatrix}$

$\begin{bmatrix} 8& 5\\ -3& 1 \end{bmatrix}$

$\begin{bmatrix} 8& 5\\ -3& -1 \end{bmatrix}$

$\begin{bmatrix} 12& 5\\ 17& 7 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 8& 5\\ -3& -1 \end{bmatrix}$

Explanation:

The first step in solving this problem is to multiply the matrix by the scalar.

$S\begin{bmatrix}a &b\\c &d\end{bmatrix}= \begin{bmatrix} Sa &Sb \\ Sc & Sd\end{bmatrix}$

$2\begin{bmatrix} 1&0\\5&2\end{bmatrix}=\begin{bmatrix} 2&0\\10&4\end{bmatrix}$

We then have to make sure we can subtract the matrices.

In order to subtract matrices, they have to be of the same dimension. In this case, they are both 2x2.

Using our new matrix from multiplying the scalar and subtracting it from our other matrix we get the following:

$\begin{bmatrix} 10 &5\\7 &3\end{bmatrix}-\begin{bmatrix} 2&0\\10&4\end{bmatrix}=\begin{bmatrix} 8&5\\-3 & -1\end{bmatrix}$

Report an Error

Example Question #3 : Find The Sum Or Difference Of Two Matrices

We consider the following matrices:

$A=\begin{bmatrix} 1 & 2 &2 \\ 1&2 &2 \\1 &2 &2 \end{bmatrix},B=\begin{bmatrix} 1 &2 & 2 &2 \\1 &2 &2 & 2\\1 &2 &2 &2 \end{bmatrix}$

Find B-A .

Possible Answers:

$\begin{bmatrix} 0 &0 &0 &2 \\0 & 0 &0 &2 \\ 0&0 &0 &2 \\ 0 &0 &0 &2 \end{bmatrix}$

$\begin{bmatrix} 0 & 0 &2 \\0 & 0 & 2\\0 &0 &2 \end{bmatrix}$

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

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

We can't find B-A .

Correct answer:

We can't find B-A .

Explanation:

To be able to subtract matrices, the matrices must have the same size.

A is 3x3 and B is 3x4. Therefore we can't perform this operation.

Report an Error

Example Question #4 : Find The Sum Or Difference Of Two Matrices

Given the following matrices, what is the product of and ?

$\begin{bmatrix} 1&-4 \\ 2&x \end{bmatrix} - \begin{bmatrix} y&4 \\ 8&1 \end{bmatrix} = \begin{bmatrix} -8&-8 \\ -6&4 \end{bmatrix}$

Possible Answers:

Correct answer:

Explanation:

When subtracting matrices, you want to subtract each corresponding cell.

$\begin{bmatrix} 1-y&-4-4 \\ 2-8&x-1 \end{bmatrix}= \begin{bmatrix} -8&-8 \\ -6&4 \end{bmatrix}$

Now solve for and

x-1=4

x=5

1-y=-8

y=9

xy = 45

Report an Error

Example Question #1 : Find The Sum Or Difference Of Two Matrices

If $\begin{bmatrix} a&b\\ c&d \end{bmatrix} + \begin{bmatrix} 3&14\\ 12&4 \end{bmatrix} = \begin{bmatrix} 19&2\\ 4&5 \end{bmatrix}$ , what is a+b+c+d ?

Possible Answers:

Correct answer:

Explanation:

You can treat matrices just like you treat other members of an equation. Therefore, you can subtract the matrix

$\begin{bmatrix} 3&14\\ 12&4 \end{bmatrix}$

from both sides of the equation. This gives you:

$\begin{bmatrix} a&b\\ c&d \end{bmatrix}=\begin{bmatrix} 19&2\\ 4&5 \end{bmatrix}-\begin{bmatrix} 3&14\\ 12&4 \end{bmatrix}$

Now, matrix subtraction is simple. You merely subtract each element, matching the correlative spaces with each other:

$\begin{bmatrix} a&b\\ c&d \end{bmatrix} = \begin{bmatrix} 19-3&2-14\\ 4-12&5-4 \end{bmatrix}$

Then, you simplify:

$\begin{bmatrix} 19-3&2-14\\ 4-12&5-4 \end{bmatrix} = \begin{bmatrix} 16&-12\\ -8&1 \end{bmatrix}$

Therefore, a+b+c+d = 16-12-8+1=-3

Report an Error

Example Question #7 : Find The Sum Or Difference Of Two Matrices

$\begin{bmatrix} -4&7 &-13 \\ 8&2 &1 \\ -11&-5 &3 \end{bmatrix}-\begin{bmatrix} -6&18 &2 \\ 1&-4 &10 \\ 9&-17 &1 \end{bmatrix}=$

Possible Answers:

$\begin{bmatrix} 10& -1& -5\\ 8& 6& -12\\ -14& 12& 4 \end{bmatrix}$

$\begin{bmatrix} -2& -4& -15\\ 7& -6& -9\\ -20& 6& 2 \end{bmatrix}$

$\begin{bmatrix} -10& -11& 13\\ -3& 4& -9\\ -2& 12& 2 \end{bmatrix}$

$\begin{bmatrix} 2& -13& -8\\ 7& 4& -9\\ -20& 12& -2 \end{bmatrix}$

$\begin{bmatrix} 2& -11& -15\\ 7& 6& -9\\ -20& 12& 2 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 2& -11& -15\\ 7& 6& -9\\ -20& 12& 2 \end{bmatrix}$

Explanation:

To find the difference between two matrices with the same dimensions, we simply subtract each entry from the right matrix from the corresponding entry of the left matrix. After performing the operation 9 times, we get the following matrix:

$\begin{bmatrix} -4&7 &-13 \\ 8&2 &1 \\ -11&-5 &3 \end{bmatrix}-\begin{bmatrix} -6&18 &2 \\ 1&-4 &10 \\ 9&-17 &1 \end{bmatrix}=\begin{bmatrix} 2& -11& -15\\ 7& 6& -9\\ -20& 12& 2 \end{bmatrix}$

Report an Error

Example Question #5 : Find The Sum Or Difference Of Two Matrices

Find the difference if it exists

$\small \begin{pmatrix} 1\\ 2\\3 \end{pmatrix}-\begin{pmatrix} 2\\2 \\ 2 \end{pmatrix} \,$

Possible Answers:

$\small DNE$

$\small \begin{pmatrix} 1\\ 0\\-1 \end{pmatrix}\,$

$\small \begin{pmatrix} 2\\ 4\\6 \end{pmatrix}$

$\begin{pmatrix} -1\\ 0\\1 \end{pmatrix}$

Correct answer:

$\begin{pmatrix} -1\\ 0\\1 \end{pmatrix}$

Explanation:

Because the two matrices have the same dimension, the difference exists

$\small \small \small \begin{pmatrix} 1\\ 2\\3 \end{pmatrix}-\begin{pmatrix} 2\\2 \\ 2 \end{pmatrix} \,=\begin{pmatrix} 1-2\\ 2-2\\3-2 \end{pmatrix}= \begin{pmatrix} -1\\ 0\\1 \end{pmatrix}$

Report an Error

Example Question #1 : Find The Sum Or Difference Of Two Matrices

$\begin{bmatrix} 9 &-2 \\ 4&-5 \end{bmatrix}-\begin{bmatrix} 4 &5 \\ -6&-3 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -5 &-7 \\ 10&-2 \end{bmatrix}$

$\begin{bmatrix} 5 &-7 \\ 1&-2 \end{bmatrix}$

$\begin{bmatrix} 5 &-7 \\ 10&-2 \end{bmatrix}$

$\begin{bmatrix} 5 &7 \\ 10&-2 \end{bmatrix}$

$\begin{bmatrix} 5 &-7 \\ 0&-2 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 5 &-7 \\ 10&-2 \end{bmatrix}$

Explanation:

To solve this problem, subtract the corresponding numbers in each matrix: ( 9-4=5, -2-5=-7, 4-(-6)=10, -5-(-3)=-2) . Then, put those answers in the corresponding places in the answer matrix, so that you get: $\begin{bmatrix} 5 &-7 \\ 10&-2 \end{bmatrix}$ .

Report an Error

Example Question #6 : Find The Sum Or Difference Of Two Matrices

Add:

$\begin{bmatrix} 11& 9\\ 7& -5 \end{bmatrix}+$ $\begin{bmatrix} 6& 9\\ 10& 13 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 17& 18\\ 17& 8 \end{bmatrix}$

$\begin{bmatrix} 17& 19\\ 16& 15 \end{bmatrix}$

$\begin{bmatrix} 35\\ 25 \end{bmatrix}$

$\begin{bmatrix} 36\\ 31 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 17& 18\\ 17& 8 \end{bmatrix}$

Explanation:

In order to add matrices, they have to be of the same dimension. In this case, they are both 2x2.

The formula to add matrices is as follows:

$\begin{bmatrix} a& b\\ c& d \end{bmatrix}+\begin{bmatrix} e& f\\ g& h \end{bmatrix}=\begin{bmatrix} a+e& b+f\\ c+g& d+h \end{bmatrix}$

Plugging in our values to solve we get:

$\begin{bmatrix} 11& 9\\ 7& -5 \end{bmatrix}+\begin{bmatrix} 6& 9\\ 10& 13 \end{bmatrix}=\begin{bmatrix} 11+6& 9+9\\ 7+10& -5+13 \end{bmatrix}=\begin{bmatrix} 17& 18\\ 17& 8 \end{bmatrix}$

Report an Error

View Pre-Calculus Tutors

Shubham
Certified Tutor

Jaypee University of Information and Technology, Bachelor of Technology, Computer Science.

View Pre-Calculus Tutors

Muhammad
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Mechanical Engineering.

View Pre-Calculus Tutors

Joseph
Certified Tutor

Rutgers University-New Brunswick, Bachelor in Arts, Chemistry. Rutgers Graduate School of Biomedical Sciences, Current Grad S...

All Precalculus Resources

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

Popular Subjects

LSAT Tutors in Atlanta, SAT Tutors in Chicago, SAT Tutors in San Francisco-Bay Area, Calculus Tutors in Dallas Fort Worth, Physics Tutors in Miami, Chemistry Tutors in Denver, Math Tutors in Dallas Fort Worth, LSAT Tutors in New York City, Spanish Tutors in Denver, LSAT Tutors in Seattle

Popular Courses & Classes

GRE Courses & Classes in Philadelphia, Spanish Courses & Classes in Atlanta, SAT Courses & Classes in Seattle, ISEE Courses & Classes in New York City, ISEE Courses & Classes in Los Angeles, LSAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Denver, Spanish Courses & Classes in Philadelphia, GMAT Courses & Classes in Miami, SSAT Courses & Classes in Atlanta

Popular Test Prep

ISEE Test Prep in Houston, GMAT Test Prep in Los Angeles, MCAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Philadelphia, SSAT Test Prep in Chicago, MCAT Test Prep in Washington DC, ISEE Test Prep in Dallas Fort Worth, LSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Washington DC, GMAT Test Prep in Philadelphia

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 Sum or Difference of Two Matrices

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Find The Sum Or Difference Of Two Matrices

Example Question #2 : Find The Sum Or Difference Of Two Matrices

Example Question #3 : Find The Sum Or Difference Of Two Matrices

Example Question #3 : Find The Sum Or Difference Of Two Matrices

Example Question #4 : Find The Sum Or Difference Of Two Matrices

Example Question #1 : Find The Sum Or Difference Of Two Matrices

Example Question #7 : Find The Sum Or Difference Of Two Matrices

Example Question #5 : Find The Sum Or Difference Of Two Matrices

Example Question #1 : Find The Sum Or Difference Of Two Matrices

Example Question #6 : Find The Sum Or Difference Of Two Matrices

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: