Call Now to Set Up Tutoring:

(888) 888-0446

Finite Mathematics : Systems of Linear Equations: Matrices

Study concepts, example questions & explanations for Finite Mathematics

Create An Account

All Finite Mathematics Resources

1 Diagnostic Test 22 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Systems Of Linear Equations: Matrices

Find the value of when,

$6\times 7\equiv n\ (\text{mod } 5)$ .

Possible Answers:

n=8

n=2

n=40

n=3

n=42

Correct answer:

n=2

Explanation:

To find the value of when,

$6\times 7\equiv n\ (\text{mod } 5)$ first multiply six and seven together.

$6\times 7=42$

Now, recall that mod means the remainder after division occurs.

In this case

$6\times 7\equiv n\ (\text{mod } 5)$

$5)\overline{42\ }$

--------------

Therefore, the remainder is two.

n=2

Report an Error

Example Question #2 : Systems Of Linear Equations: Matrices

The following tables describe matrix operations.

$\begin{tabular}{ c|cc } \$ & * & \% \\ \hline * & \%& * \\ \% & * & * \\ \end{tabular}$ $\begin{tabular}{ c|cc } \# & \%& * \\ \hline \% & *& \% \\ * & \% & * \\ \end{tabular}$

Calculate the following using the tables from above.

$(\%\ \#\ \%)\ \$\ \%$

Possible Answers:

*^2

$\#$

$\$$

$\%$

Correct answer:

Explanation:

This question is testing the matrix operation. Remember to use order of operations and perform the algebraic operation that is inside the parentheses first.

$(\%\ \#\ \%)\ \$\ \%$

First look at the # table.

$\begin{tabular}{ c|cc } \# & \%& * \\ \hline \% & *& \% \\ * & \% & * \\ \end{tabular}$

Multiplying % by % results in *.

Now go to the $ table and multiply * by %.

$\begin{tabular}{ c|cc } \$ & * & \% \\ \hline * & \%& * \\ \% & * & * \\ \end{tabular}$

$*\ \$\ \%=*$

Therefore,

$(\%\ \#\ \%)\ \$\ \%=*$

Report an Error

Example Question #3 : Systems Of Linear Equations: Matrices

Find the value of when,

$3\times 9\equiv n\ (\text{mod } 4)$ .

Possible Answers:

n=0

n=6

n=2

n=4

n=3

Correct answer:

n=3

Explanation:

To find the value of when,

$3\times 9\equiv n\ (\text{mod } 4)$ first multiply three and nine together.

$3\times 9=27$

Now, recall that mod means the remainder after division occurs.

In this case

$3\times 9\equiv n\ (\text{mod } 4)$

$4)\overline{27\ }$

--------------

Therefore, the remainder is three.

n=3

Report an Error

Example Question #1 : Finite Mathematics

$A = \begin{bmatrix} 3 & -1 \\ -2 & 4 \end{bmatrix}$

Give the determinant of .

Possible Answers:

Correct answer:

Explanation:

The determinant of a two-by-two matrix

$A= \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$

can be found by evaluating the expression

$\det A = a_{11}a_{22} - a_{12}a_{23}$

Substitute the corresponding elements to get

$\det A = 3(4)- (-1)(-2) = 12 - 2 = 10$ .

Report an Error

Example Question #9 : Finite Mathematics

Consider the system of linear equations:

x + 8y = 120

-4x + 32y = 240

What kind of system is this?

Possible Answers:

Dependent

Consistent and independent

Inconsistent

Correct answer:

Consistent and independent

Explanation:

One way to identify whether the matrix is consistent and independent is to form a matrix of its variable coefficients, and calculate its determinant. The matrix is

$A = \begin{bmatrix} 1 & 8 \\ -4 & 32 \end{bmatrix}$

The determinant of a two-by-two matrix

$A= \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$

can be found by evaluating the expression

$\det A = a_{11}a_{22} - a_{12}a_{23}$

Substitute the corresponding elements to get

$\det A = 1(32)- 8(-4) = 32 -(-32) = 64$

Since $\det A \ne 0$ ,

it follows that the system is consistent and independent.

Report an Error

Example Question #1 : Systems Of Linear Equations: Matrices

$B = \begin{bmatrix} 3 & 2 \\ 4 & 3 \end{bmatrix}$

Which of the following is equal to $B^{-1}$ ?

Possible Answers:

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

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

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

$\begin{bmatrix} 3 & 4 \\ 2 & 3 \end{bmatrix}$

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

Correct answer:

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

Explanation:

$B^{-1}$ , the inverse of a two-by-two matrix

$B = \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix}$ ,

can be calculated as follows:

$B^{-1} = \frac{1}{D} \begin{bmatrix} b_{22} & -b_{12} \\ -b_{21} & b_{11} \end{bmatrix}$ ,

where $D = b_{11}b_{22} - b_{12} b_{21}$ .

Setting each of the values accordingly,

D = 3(3)- 2(4) = 9 - 8 = 1

$B^{-1} = \frac{1}{1} \begin{bmatrix} 3& -2 \\ -4 & 3 \end{bmatrix}$ , or

$B^{-1} = \begin{bmatrix} 3& -2 \\ -4 & 3 \end{bmatrix}$ .

Report an Error

Example Question #1 : Systems Of Linear Equations: Matrices

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

refers to the two-by-two identity matrix.

Which of the following expressions is equal to A+ I ?

Possible Answers:

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

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

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

A+ I is undefined.

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

Correct answer:

A+ I is undefined.

Explanation:

For the sum of two matrices to be defined, they must have the same number of rows and columns. is a matrix with three columns; since, in this problem, refers to the two-by-two identity matrix

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

has two columns. Since the number of columns differs, A+ I is undefined.

Report an Error

Example Question #11 : Finite Mathematics

is a three-by-four matrix.

Which must be true?

Possible Answers:

None of the statements in the other choices must be true.

has four rows.

has three rows.

has four rows.

has three rows.

Correct answer:

has three rows.

Explanation:

The product of two matrices and , where has rows and columns and has rows and columns, is a matrix with rows and columns. It follows that must have the same number of rows as . Since has three rows, so does . Nothing can be inferred about the number of rows of .

Report an Error

Example Question #1 : Systems Of Linear Equations: Matrices

$K = \begin{bmatrix} 1 & -2 & 3 \\ -4 & 2 & 1 \\ 2 & 1 & 3 \end{bmatrix}$

True or false:

$7K = \begin{bmatrix} 7 & -14 & 21 \\ -4 & 2 & 1 \\ 2 & 1 & 3 \end{bmatrix}$

Possible Answers:

False

True

Correct answer:

False

Explanation:

The product of any scalar value and a matrix is the matrix formed when each entry in the matrix is multiplied by that scalar. Thus, if

$K = \begin{bmatrix} 1 & -2 & 3 \\ -4 & 2 & 1 \\ 2 & 1 & 3 \end{bmatrix}$

then

$7K = \begin{bmatrix} 7 (1) & 7 ( -2 )& 7(3) \\ 7(-4) & 7(2) & 7(1) \\ 7(2) & 7(1) & 7(3) \end{bmatrix}$

$= \begin{bmatrix} 7& -14 & 21 \\ -28 & 14 & 7 \\ 14 & 7 & 21 \end{bmatrix}$

This is not equal to the matrix

$\begin{bmatrix} 7 & -14 & 21 \\ -4 & 2 & 1 \\ 2 & 1 & 3 \end{bmatrix}$ ,

since the entries in the second and third rows differ. The statement is false.

Report an Error

Example Question #1 : Systems Of Linear Equations: Matrices

$\begin{bmatrix} 14 \\ 25 \end{bmatrix} = \begin{bmatrix} x + y \\ x - y \end{bmatrix}$

True or false: there is no solution (x,y) that makes this matrix equation true.

Possible Answers:

True

False

Correct answer:

False

Explanation:

For two matrices to be equal, two conditions must hold:

1) The matrices must have the same dimension. This can be seen to be the case, since both matrices have two rows and one column.

2) All corresponding entries must be equal. For this to happen, it must hold that

x+y=14

x-y=25

This is a system of two equations in two variables, which can be solved as follows:

Add both sides of the equations:

$\begin{matrix} x+y=14 \\ \underline{x-y=25} \\ 2x\; \; \; \; \; = 39 \end{matrix}$

It follows that

x = 19.5

Substitute back:

x+y=14

19.5+y=14

y = -5.5

Thus, there exists a solution to the system, and, consequently, to the original matrix equation. The statement is therefore false.

Report an Error

View Tutors

Crystal
Certified Tutor

University of California-Davis, Bachelor of Science, Civil Engineering.

View Tutors

Kailey
Certified Tutor

University of San Francisco, Master of Arts Teaching, Education.

View Tutors

Ekta
Certified Tutor

Punjab Agricultural University, India, Doctorate (PhD), Chemistry.

All Finite Mathematics Resources

1 Diagnostic Test 22 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Dallas Fort Worth, Spanish Tutors in Miami, Spanish Tutors in Los Angeles, Calculus Tutors in Seattle, ISEE Tutors in San Francisco-Bay Area, Biology Tutors in Dallas Fort Worth, GRE Tutors in New York City, Physics Tutors in Chicago, GMAT Tutors in San Diego, SAT Tutors in Boston

Popular Courses & Classes

ACT Courses & Classes in San Diego, GRE Courses & Classes in Philadelphia, SSAT Courses & Classes in Houston, SSAT Courses & Classes in Miami, GRE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Los Angeles, Spanish Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in New York City, GRE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Philadelphia

Popular Test Prep

ACT Test Prep in Boston, ACT Test Prep in San Diego, LSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Boston, ACT Test Prep in Washington DC, ISEE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Philadelphia, GRE Test Prep in Seattle, SSAT Test Prep in Houston, MCAT Test Prep in Phoenix

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

Finite Mathematics : Systems of Linear Equations: Matrices

Study concepts, example questions & explanations for Finite Mathematics

All Finite Mathematics Resources

Example Questions

Example Question #1 : Systems Of Linear Equations: Matrices

Example Question #2 : Systems Of Linear Equations: Matrices

Example Question #3 : Systems Of Linear Equations: Matrices

Example Question #1 : Finite Mathematics

Example Question #9 : Finite Mathematics

Example Question #1 : Systems Of Linear Equations: Matrices

Example Question #1 : Systems Of Linear Equations: Matrices

Example Question #11 : Finite Mathematics

Example Question #1 : Systems Of Linear Equations: Matrices

Example Question #1 : Systems Of Linear Equations: Matrices

All Finite Mathematics Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: