Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Scalar interactions with Matrices

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Matrices

Evaluate: $-3\begin{bmatrix} 2& 3 & 4\\ 4&-5 & 10 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -12&-6 \\ 15& -9\\ -30&-12 \end{bmatrix}$

$\begin{bmatrix} -6& -9& -12\\ -12& 15& -30 \end{bmatrix}$

$\begin{bmatrix} -1& 0& 1\\ -12& 15&-30 \end{bmatrix}$

$\begin{bmatrix} -18& 6& -42 \end{bmatrix}$

$\begin{bmatrix} -12& -1\\ 15& 0\\ -30& 1 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -6& -9& -12\\ -12& 15& -30 \end{bmatrix}$

Explanation:

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.

$-3\begin{bmatrix} 2& 3 & 4\\ 4&-5 & 10 \end{bmatrix}=\begin{bmatrix} -6&-9 &-12 \\ -12& 15&-30 \end{bmatrix}$

Report an Error

Example Question #1 : Multiplication Of Matrices

$5\begin{bmatrix} a \\ b \end{bmatrix} = 14\begin{bmatrix} 20 \\ 12 \end{bmatrix}$

What is a+b ?

Possible Answers:

$\frac{191}{4}$

$\frac{148}{5}$

$\frac{41}{5}$

$\frac{448}{5}$

Correct answer:

$\frac{448}{5}$

Explanation:

You can begin by treating this equation just like it was:

5x=14y

That is, you can divide both sides by :

$\begin{bmatrix} a \\ b \end{bmatrix} = \frac{14}{5}\begin{bmatrix} 20 \\ 12 \end{bmatrix}$

Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:

$\begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} \frac{14}{5}*20 \\ \frac{14}{5}*12 \end{bmatrix}$

Then, simplify:

$\begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} 56 \\ \frac{168}{5} \end{bmatrix}$

Therefore, $a+b=56+\frac{168}{5}=\frac{280}{5}+\frac{168}{5}=\frac{448}{5}$

Report an Error

Example Question #2 : Matrices

If $\frac{1}{2}$\bigl(\begin{smallmatrix} 2a\\4b \end{smallmatrix} \bigr)$=$\bigl(\begin{smallmatrix} 53 \\ 98 \end{smallmatrix} \bigr)$$ , what is a+b ?

Possible Answers:

$\frac{103}{2}$

$\frac{99}{2}$

102

Correct answer:

102

Explanation:

Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :

$\frac{1}{2}\begin{bmatrix} 2a\\4b \end{bmatrix}=\begin{bmatrix} a\\2b \end{bmatrix}$

Now, this means that your equation looks like:
$\begin{bmatrix} a\\2b \end{bmatrix}=\begin{bmatrix} 53 \\ 98 \end{bmatrix}$

This simply means:

a=53

and

2b=98 or b=49

Therefore, a+b=53+49=102

Report an Error

Example Question #1 : Matrices

Simplify:

$\begin{bmatrix} 13 & 4\\ 71 &3 \end{bmatrix} + 4\begin{bmatrix} 5 & 3\\ 11 &22 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 33 & 16\\ 115 & 91\end{bmatrix}$

$\begin{bmatrix} 20 & 12\\ 44 &88 \end{bmatrix}$

$\begin{bmatrix} 31 & 93\\ 3 &21 \end{bmatrix}$

$\begin{bmatrix} 49\\ 206\end{bmatrix}$

$\begin{bmatrix} 49 & 206\end{bmatrix}$

Correct answer:

$\begin{bmatrix} 33 & 16\\ 115 & 91\end{bmatrix}$

Explanation:

Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:

$\begin{bmatrix} 13 & 4\\ 71 &3 \end{bmatrix} + 4\begin{bmatrix} 5 & 3\\ 11 &22 \end{bmatrix}= \begin{bmatrix} 13 & 4\\ 71 &3 \end{bmatrix}+\begin{bmatrix} 20 & 12\\ 44 &88 \end{bmatrix}$

The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.

$\begin{bmatrix} 13 & 4\\ 71 &3 \end{bmatrix} + \begin{bmatrix} 20 & 12\\ 44 &88 \end{bmatrix} = \begin{bmatrix} 13 +20 & 4+12\\ 71+44 &3 +88\end{bmatrix}$

$\begin{bmatrix} 13 +20 & 4+12\\ 71+44 &3 +88\end{bmatrix}= \begin{bmatrix} 33 & 16\\ 115 & 91\end{bmatrix}$

Report an Error

Example Question #1 : Matrices

Simplify the following

$3\cdot \begin{bmatrix} -3& 5&0 \\ 4& -1& 2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -9& 5&0 \\ 12& -1& 2 \end{bmatrix}$

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

$\begin{bmatrix} -9& 15&0 \\ 12& -3& 6 \end{bmatrix}$

$\begin{bmatrix} 6 \\ 15 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -9& 15&0 \\ 12& -3& 6 \end{bmatrix}$

Explanation:

When multplying any matrix by a scalar quantity (3 in our case), we simply multiply each term in the matrix by the scalar.

Therefore, every number simply gets multiplied by 3, giving us our answer.

$\begin{bmatrix} -9& 15&0 \\ 12& -3& 6 \end{bmatrix}$

Report an Error

Example Question #5 : Scalar Interactions With Matrices

Define matrix $M = \begin{bmatrix} 3&-5 &4 \\ 5&6 &1 \\ 3&-4 & -7 \end{bmatrix}$ , and let be the 3x3 identity matrix.

If N = M -6 I , then evaluate $n _{3,1}$ .

Possible Answers:

Correct answer:

Explanation:

The 3x3 identity matrix is

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

Both scalar multplication of a matrix and matrix addition are performed elementwise, so

$n _{3,1} = m _{3,1} -6 i _{3,1}$

$m _{3,1}$ is the first element in the third row of , which is 3; similarly, $i _{3,1} = 0$ . Therefore,

$n _{3,1} = 3 -6 (0)= 3$

Report an Error

Example Question #1 : Matrices

Define matrix $M = \begin{bmatrix} 3&-5 &4 \\ 5&6 &1 \\ 3&-4 & -7 \end{bmatrix}$ , and let be the 3x3 identity matrix.

If N = 7M + I , then evaluate $n _{3,1}$ .

Possible Answers:

Correct answer:

Explanation:

The 3x3 identity matrix is

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

Both scalar multplication of a matrix and matrix addition are performed elementwise, so

$n _{3,1} = 7 m _{3,1} + i _{3,1}$

$m _{3,1}$ is the first element in the third row of , which is 3; similarly, $i _{3,1} = 0$ . Therefore,

$n _{3,1} = 7 (3) + 0 = 21$

Report an Error

Example Question #5 : Matrices

Define matrix $M = \begin{bmatrix} 3&-5 &4 \\ 5&6 &1 \\ 3&-4 & -7 \end{bmatrix}$ .

If 5N = M , evaluate $n_{2,1}$ .

Possible Answers:

The correct answer is not among the other responses.

Correct answer:

Explanation:

If 5N = M , then $N = \frac{1}{5} M$ .

Scalar multplication of a matrix is done elementwise, so

$n_{2,1} = \frac{1}{5} m_{2,1}$

$m_{2,1}$ is the first element in the second row of , which is 5, so

$n_{2,1} = \frac{1}{5} (5) = 1$

Report an Error

Example Question #2 : Matrices

Define matrix $M = \begin{bmatrix} 3&-5 &4 \\ 5&6 &1 \\ 3&-4 & -7 \end{bmatrix}$ .

If N = 3M , evaluate $n_{2,3}$ .

Possible Answers:

$-1\frac{1}{3}$

The correct answer is not among the other responses.

$\frac{1}{3}$

Correct answer:

Explanation:

Scalar multplication of a matrix is done elementwise, so

$n_{2,3} = 3 m _{2,3}$

$m _{2,3}$ is the third element in the second row of , which is 1, so

$n_{2,3} = 3 \cdot 1 = 3$

Report an Error

Example Question #1 : Matrices

Define matrix $M = \begin{bmatrix} 3&-5 &4 \\ 5&6 &1 \\ 3&-4 & -7 \end{bmatrix}$ , and let be the 3x3 identity matrix.

If M = 4N + I , evaluate $n_{2,1}$ .

Possible Answers:

$-1\frac{1}{2}$

The correct answer is not given among the other responses.

$-1\frac{1}{4}$

$1\frac{1}{4}$

Correct answer:

$1\frac{1}{4}$

Explanation:

The 3x3 identity matrix is

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

Both scalar multplication of a matrix and matrix addition are performed elementwise, so

$m_{2,1} = 4n_{2,1} +i_{2,1}$

$m_{2,1}$ is the first element in the second row, which is 5; similarly, $i_{2,1} = 0$ . The equation becomes

$5= 4n_{2,1} +0$

$5= 4n_{2,1}$

$n_{2,1}= 5 \div 4 = 1\frac{1}{4}$

Report an Error

View ACT Math Tutors

Anne
Certified Tutor

University of Maryland-Baltimore, Doctor of Science, Accounting.

View ACT Math Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View ACT Math Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

ACT Courses & Classes in Los Angeles, Spanish Courses & Classes in Chicago, GRE Courses & Classes in Boston, MCAT Courses & Classes in Chicago, GRE Courses & Classes in Los Angeles, ISEE Courses & Classes in San Diego, SSAT Courses & Classes in Atlanta, ISEE Courses & Classes in New York City, SAT Courses & Classes in San Diego, GRE Courses & Classes in Phoenix

Popular Test Prep

ISEE Test Prep in Boston, ISEE Test Prep in Seattle, ACT Test Prep in Seattle, ACT Test Prep in Los Angeles, ACT Test Prep in Houston, GRE Test Prep in Phoenix, SSAT Test Prep in Los Angeles, LSAT Test Prep in New York City, ISEE Test Prep in Chicago, ACT Test Prep in Chicago

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

ACT Math : Scalar interactions with Matrices

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Matrices

Example Question #1 : Multiplication Of Matrices

Example Question #2 : Matrices

Example Question #1 : Matrices

Example Question #1 : Matrices

Example Question #5 : Scalar Interactions With Matrices

Example Question #1 : Matrices

Example Question #5 : Matrices

Example Question #2 : Matrices

Example Question #1 : Matrices

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: