Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Find the Sum of Two Matrices

Study concepts, example questions & explanations for Precalculus

CREATE AN ACCOUNT Create Tests & Flashcards

Home Embed

All Precalculus Resources

12 Diagnostic Tests 400 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 Next →

Example Question #1 : Addition Of Matrices

Add:

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

Possible Answers:

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

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

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

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

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

Example Question #1 : Addition Of Matrices

Add:

$3\begin{bmatrix} 2& 0\\ 1& 4 \end{bmatrix}+$ $\begin{bmatrix} 2& 7\\ 5& 1 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 24& 21\\ 18& 15 \end{bmatrix}$

$\begin{bmatrix} 4& 7\\ 6& 5 \end{bmatrix}$

$\begin{bmatrix} 8& 7\\ 8& 13 \end{bmatrix}$

$\begin{bmatrix} 12& 21\\ 18& 15 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 8& 7\\ 8& 13 \end{bmatrix}$

Explanation:

The first step in solving this problem is to multiply the matrix by the scalar. The formula is as follows:

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

$3 \begin{bmatrix}2 &0 \\1 &4 \end{bmatrix} =\begin{bmatrix} 3(2)&3(0)\\3(1)& 3(4)\end{bmatrix}= \begin{bmatrix} 6 &0 \\3 &12\end{bmatrix}$

In order to add matrices, they have to be of the same dimension.

In this case, they are both 2x2. So, we can then add the matrices together. The result is as follows:

$\begin{bmatrix} 6 &0\\3 &12\end{bmatrix}+\begin{bmatrix} 2 & 7 \\5 &1 \end{bmatrix}=\begin{bmatrix} 6+2 &0+7\\3+5& 12+1\end{bmatrix}$

$=\begin{bmatrix} 8 &7\\8&13\end{bmatrix}$

Report an Error

Example Question #3 : Addition Of Matrices

We consider and defined as follows where they are supposed to be of order .

$A=\begin{bmatrix} 1 & 2 & 3 &\cdots & n\\ 1 &2 &3 &\cdots &n \\ 1& 2 &3 &\cdots & n\\ \vdots&\vdots &\vdots &\vdots &\vdots \\ 1& 2 &3 &\cdots &n \end{bmatrix}$ $B=\begin{bmatrix} n&n-1 &n-2 &\cdots &1 \\ n&n-1 &n-2 &\cdots &1\\\vdots & \vdots&\vdots &\vdots &\vdots \\ n&n-1 &n-2 &\cdots &1\\ n&n-1 &n-2 &\cdots &1 \end{bmatrix}$

What is the sum of and ?

Possible Answers:

$\begin{bmatrix}\frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} \\ \frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} \\\frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} \\ \vdots &\vdtos &\vdots &\vdots &\vdots \\ \frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} &\frac{n+1}{2} \end{bmatrix}$

$\begin{bmatrix}n+2 &n+2 &n+2 &n+2 &n+2 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ \vdots &\vdtos &\vdots &\vdots &\vdots \\ n+1 &n+1 &n+1 &n+1 &n+1 \end{bmatrix}$

$\begin{bmatrix}n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ \vdots &\vdtos &\vdots &\vdots &\vdots \\ n-1 &n-1 &n-1 &n-1 &n-1 \end{bmatrix}$

$\begin{bmatrix}n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ \vdots &\vdtos &\vdots &\vdots &\vdots \\ n+2 &n+2 &n+2 &n+2 &n+2 \end{bmatrix}$

$\begin{bmatrix}n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ \vdots &\vdtos &\vdots &\vdots &\vdots \\ n+1 &n+1 &n+1 &n+1 &n+1 \end{bmatrix}$

Correct answer:

$\begin{bmatrix}n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ \vdots &\vdtos &\vdots &\vdots &\vdots \\ n+1 &n+1 &n+1 &n+1 &n+1 \end{bmatrix}$

Explanation:

We can perform the addition since the matrices have the same sizes.

$A+B=\begin{bmatrix} 1 & 2 & 3 &\cdots & n\\ 1 &2 &3 &\cdots &n \\ 1& 2 &3 &\cdots & n\\ \vdots&\vdots &\vdots &\vdots &\vdots \\ 1& 2 &3 &\cdots &n \end{bmatrix}+$ $\begin{bmatrix} n&n-1 &n-2 &\cdots &1 \\ n&n-1 &n-2 &\cdots &1\\\vdots & \vdots&\vdots &\vdots &\vdots \\ n&n-1 &n-2 &\cdots &1\\ n&n-1 &n-2 &\cdots &1 \end{bmatrix}$

Looking at the first row of entries we get:

$\begin{bmatrix} 1+n & 2+n-1=1+n & 3+n-2=1+n ...\end{bmatrix}$

Note that any entry in the sum of A+B is equal to n+1 .

Thus the sum becomes:

$\begin{bmatrix}n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ n+1 &n+1 &n+1 &n+1 &n+1 \\ \vdots &\vdtos &\vdots &\vdots &\vdots \\ n+1 &n+1 &n+1 &n+1 &n+1 \end{bmatrix}$

Report an Error

Example Question #1 : Find The Sum Of Two Matrices

We consider the matrices and of the same size .

$A=\begin{bmatrix} 1 &1 &\cdots &1 \\ 1&1 &\cdots &1 \\ \vdots &\vdots &\vdots &\vdots \\ 1& 1&\cdots &1 \end{bmatrix},B=\begin{bmatrix} 1 &-1 &\cdots &-1 \\ 1&-1 &\cdots &-1 \\ \vdots &\vdots &\vdots &\vdots \\ 1& -1&\cdots &-1 \end{bmatrix}$

Find the sum A+B .

Possible Answers:

$A+B=\begin{bmatrix} 1 &0 &\cdots &-1 \\ 1&0 &\cdots &-1 \\ \vdots &\vdots &\vdots &\vdots \\ 1& 0&\cdots &-1 \end{bmatrix}$

$A+B=\begin{bmatrix} 0&0 &\cdots &0\\ 0&0 &\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 0& 0&\cdots &0 \end{bmatrix}$

$A+B=\begin{bmatrix} 2 &1 &\cdots &1 \\ 2&1 &\cdots &1 \\ \vdots &\vdots &\vdots &\vdots \\ 2& 1&\cdots &1 \end{bmatrix}$

$A+B=\begin{bmatrix} 2 &1 &\cdots & 0\\ 1&1 &\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 2& 1&\cdots &1 \end{bmatrix}$

$A+B=\begin{bmatrix} 2&0&\cdots &0 \\ 2&0&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 2& 0&\cdots &0 \end{bmatrix}$

Correct answer:

$A+B=\begin{bmatrix} 2&0&\cdots &0 \\ 2&0&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 2& 0&\cdots &0 \end{bmatrix}$

Explanation:

Note: For addition of matrices, we do it componentwise.

Note: Adding the first two columns of and we obtain for every row of the first column of the resulting matrix.

In all other case, we obtain 0 everywhere. This gives the matrix:

$A+B=\begin{bmatrix} 2&0&\cdots &0 \\ 2&0&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 2& 0&\cdots &0 \end{bmatrix}$

Report an Error

Example Question #1 : Find The Sum Of Two Matrices

We will consider the two matrices and given below. and are of the same size.

$A=\begin{bmatrix} 2&0&\cdots &0 \\ 2&2&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 2& 2&\cdots &2\end{bmatrix},B= \begin{bmatrix} -2&0&\cdots &0 \\ -2&-2&\cdots &0 \\ \cdots &\cdots &\cdots &\cdots \\-2&-2&-2&-2\\\ 2& 2&\cdots &2 \end{bmatrix}$

Find the sum A+B.

Possible Answers:

$A+B=\begin{bmatrix} 0&0&\cdots &0 \\ 0&0&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 4& 4&\cdots &4 \end{bmatrix}$

$A+B=\begin{bmatrix} 0&0&\cdots &0 \\ 0&0&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 0& 4&\cdots &4 \end{bmatrix}$

$A+B=\begin{bmatrix} 0&0&\cdots &0 \\ 0&0&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 0& 0&\cdots &4 \end{bmatrix}$

$A+B=\begin{bmatrix} 0&0&\cdots &0 \\ 0&0&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 0& 0&\cdots &0 \end{bmatrix}$

$A+B=\begin{bmatrix} 0& 0 &\cdots & 0 \\ &0&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 0& 2&\cdots &0 \end{bmatrix}$

Correct answer:

$A+B=\begin{bmatrix} 0&0&\cdots &0 \\ 0&0&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 4& 4&\cdots &4 \end{bmatrix}$

Explanation:

Adding componentwise (adding entry by entry) we obtain zeros everywhere except for the last row where we get 2+2 to obain in every component of the row.

This gives the matrix:

$A+B=\begin{bmatrix} 0&0&\cdots &0 \\ 0&0&\cdots &0 \\ \vdots &\vdots &\vdots &\vdots \\ 4& 4&\cdots &4 \end{bmatrix}$

Report an Error

Example Question #1 : Find The Sum Of Two Matrices

We consider the two matrice, find the sum A+B .

$A=\begin{bmatrix} 1 &2 & 3 &4 &5 \end{bmatrix},B=\begin{bmatrix} 1 &2 & 3 &4 &5 \end{bmatrix}$

Possible Answers:

$A+B=\begin{bmatrix} 1 &4 & 6 &8 &10 \end{bmatrix}$

$A+B=\begin{bmatrix} 2 &4 & 6 &8 &0 \end{bmatrix}$

$A+B=\begin{bmatrix} 2 &4 & 6 &8 &10 \end{bmatrix}$

We can't add A and B since they are not matrices

$A+B=\begin{bmatrix} 2 &4 & 0 &8 &10 \end{bmatrix}$

Correct answer:

$A+B=\begin{bmatrix} 2 &4 & 6 &8 &10 \end{bmatrix}$

Explanation:

Since A and B have the same size, we can perform addition.

The addition is performed componentwise.

The entry located at (i,j) of matrix A is added to the entry located at (i,j) of the matrix B.

In this case i=1 and j=1, 2 ,3 ,4,5

performing this operation we obtain:

$\begin{bmatrix} 2 &4 & 6 &8 &10 \end{bmatrix}$

Report an Error

Example Question #1 : Find The Sum Of Two Matrices

We consider the matrices and given below. Find the sum A+B .

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

Possible Answers:

We can't perform this addition.

$\begin{bmatrix} 1\\1 \\ 2 \\ 1\\ 1 \end{bmatrix}$

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

$\begin{bmatrix} 2\\1 \\ 1 \\ 1\\ 1 \end{bmatrix}$

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

Correct answer:

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

Explanation:

Since A and B have the same size, we can perform addition.

The addition is performed componentwise.

The entry located at (i,j) of matrix A is added to the entry located at (i,j) of the matrix B.

Performing this operation we obtain:

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

Report an Error

Example Question #8 : Addition Of Matrices

For the matrices below, find the sum A+B ( and are assumed to have the same size) . is assumed to be an odd positive integer.

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

$B=\begin{bmatrix} (-1)^m& (-1)^m & (-1)^m & (-1)^m \\ \vdots&\vdots &\vdots &\vodts \\ (-1)^m & (-1)^m & (-1)^m & (-1)^m \\ (-1)^m& (-1)^m & (-1)^m & (-1)^m \end{bmatrix}$

Possible Answers:

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

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

$\begin{bmatrix} -2 &-2 &-2 &-2 \\ -2 &-2 &-2 &-2 \\ \vdots& \vdots& \vdots& \vdots\\-2 &-2 &-2 &-2 \end{bmatrix}$

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

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

Correct answer:

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

Explanation:

Since we are assuming that the two matrices have the same size, we can performthe matrices addition.

We know that when adding matrices, we add them componenwise. Let (i,j) be any entry of the addition matrix. We add the entry from A to the entry from B:

since the entries from A are the same and given by 1 and the entries from B are the same and given by (-1)^m , we add these two to obtain :

1+(-1)^m and we know that m is odd integer, hence (-1)^m=-1 .

Therefore the entry of the sum matrix is 0

Therefore our matrix is given by:

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

Report an Error

Example Question #11 : Matrices

Simplify:

$\begin{bmatrix} 14&22\\ -3 &4 \end{bmatrix}+\begin{bmatrix} -3&12\\ 5 &-10 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 17&10\\ -8 &14 \end{bmatrix}$

$\begin{bmatrix} 17 & -5 \\ 3 & 1 \end{bmatrix}$

$\begin{bmatrix} 45&-4 \end{bmatrix}$

$\begin{bmatrix} 11&34\\ 2 &-6 \end{bmatrix}$

$\begin{bmatrix} 13\\ 28 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 11&34\\ 2 &-6 \end{bmatrix}$

Explanation:

Matrix addition is very easy! All that you need to do is add each correlative member to each other. Think of it like this:

$\begin{bmatrix} 14&22\\ -3 &4 \end{bmatrix}+\begin{bmatrix} -3&12\\ 5 &-10 \end{bmatrix}=\begin{bmatrix} 14-3&22+12\\ -3+5 &4-10 \end{bmatrix}$

Now, just simplify:

$\begin{bmatrix} 11&34\\ 2 &-6 \end{bmatrix}$

There is your answer!

Report an Error

Example Question #1 : How To Add Matrices

Simplify:

$\begin{bmatrix} -5&7\\ 102 & -12 \end{bmatrix}+\begin{bmatrix} 3&107\\ -10 & -9 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -8&-100\\ 112 & -3 \end{bmatrix}$

$\begin{bmatrix} -2&114\\ 92 & -21 \end{bmatrix}$

$\begin{bmatrix} 112 & 71\end{bmatrix}$

$\begin{bmatrix} 112\\ 71 \end{bmatrix}$

$\begin{bmatrix} 90\\ 93 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -2&114\\ 92 & -21 \end{bmatrix}$

Explanation:

Matrix addition is really easy—don't overthink it! All you need to do is combine the two matrices in a one-to-one manner for each index:

$\begin{bmatrix} -5&7\\ 102 & -12 \end{bmatrix}+\begin{bmatrix} 3&107\\ -10 & -9 \end{bmatrix}=\begin{bmatrix} -5+3&7+107\\ 102-10 & -12-9 \end{bmatrix}$

Then, just simplify all of those simple additions and subtractions:

$\begin{bmatrix} -5+3&7+107\\ 102-10 & -12-9 \end{bmatrix}=\begin{bmatrix} -2&114\\ 92 & -21 \end{bmatrix}$

Report an Error

← Previous 1 2 Next →

View Pre-Calculus Tutors

Chase
Certified Tutor

Unversity of Texas at San Antonio, Bachelor of Science, Biomedical Engineering.

View Pre-Calculus Tutors

Devon
Certified Tutor

CUNY John Jay College of Criminal Justice, Bachelor of Science, Forensic Psychology.

View Pre-Calculus Tutors

Elias
Certified Tutor

University of Georgia, Bachelor of Science, Mathematics.

All Precalculus Resources

12 Diagnostic Tests 400 Practice Tests Question of the Day Flashcards Learn by Concept

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 of Two Matrices

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Addition Of Matrices

Example Question #1 : Addition Of Matrices

Example Question #3 : Addition Of Matrices

Example Question #1 : Find The Sum Of Two Matrices

Example Question #1 : Find The Sum Of Two Matrices

Example Question #1 : Find The Sum Of Two Matrices

Example Question #1 : Find The Sum Of Two Matrices

Example Question #8 : Addition Of Matrices

Example Question #11 : Matrices

Example Question #1 : How To Add Matrices

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

FIND THE BEST TUTORS

Email address:
Your name:

Email address:
Your name:
Feedback: