Ask Question, Ask an Expert


Ask Math Expert

Home >> Math


For problems 1 and 2:     
Let A be a 4x4 matrix composed of all 0s.     
Let B be a 4x4 matrix composed of all 1s.

1. A NAND B = all 0s.

True or False

2. A XOR B = all 1s.        

True or False    

3. The first nine digits of a book's ISBN-10 identifier  is 0-441-27206.  The tenth digit (the check digit) is 5.

True or False

4. The binary search algorithm has a smaller "Big(O)" notation than the linear search algorithm and is, therefore, the more  efficient algorithm.     

True or False

5. Given:

Matrix A is of the form 5 x 4     
Matrix B is of the form 4 x 2     
Matrix C is of the form 2 x 5
B x C x A  has the form 5 x 5.

True or False

6. A Tautology is always true except when null sets are  involved.

True or False

7.  Given: A = {0,4,6,9,10} and B = {0,6,7,9,12}.

The Cartesian Product of A and B contains 25 valid elements since {0,0}, the NULL SET, is included in the total.

True or False

8. The cardinality of the power set {NULL, a, {NULL}, {{NULL}}}  is 3.  Note: {NULL} indicates the null (empty) set.

True or False  

9.  log(BASE2)10 = 3.3219 and log(BASE2)100 = 6.6439.

True or False

10. The matrix MEET is functionally the same as a matrix AND.

True or False

11.  Using Relations f and g, it is possible that that fog = gof in most cases.

True or False  

12.  Using Set Identities, we can deduce that:


True or False    

13.  Log(Base10)100 = 2; log 100(Base2) = 9.96

True or False

14.  To be invertible, the involved functions must map one-to-one and onto.

True or False


SHOW ALL WORK (within reason) in intermediate steps.  Solutions without intermediate work will be graded as zero.
Clearly identify each answer.     

1. Define A*B where:     

          A =  | 3 -3  6 |          B = |  6   1 |     
                  | 0  4  2 |                |  0  -5 |
                                                |  0   3 |    
2. Given A and B

           A =  |  1  0  1  |         B =        |  1  1  0  |     
                  |  1  1  0  |                      |  0  1  1  |     
                  |  0  1  0  |                      | 1  1  0   |     


A).   A  MEET  B     

B).   A  JOIN  B     

3. Given A = -2*x^3 - 5x where x = (-0.3, 0, 0.3, 1.4).  Determine:



4. Define the "Big O" function of:

F(x) = 4x*log(x^2 + 7)  +  5*[(4 + x^5) * log(x^7)+ 12]

5. Define the value of:

a)  SIGMA (2*i) where i has the range i = 0 to 3.

b)  PI (k + 4) where k has the range k = 0 to 3.

6. Define the values in the double sigma expression:

SIGMA1 SIGMA2 (3*i*j) where SIGMA1 has the range of j= 0 to 3, and where SIGMA2 has the range of i= 1 to 3.

7. Let A = (a,b,c,e,f,g,k) and B = (a,b,c,e,h,i,j).  Determine:

a)  A INT B

b)  B – A

c)  A – B

8. Let g be a function from the set G = {1,2,3,...34,35,36).  Let f be a function from the set F = {1,2,3,...34,35,36}.  Set G and F contain 36 identical elements (a – z and 0 - 9).  A partial representation of the G and F relationships are:

g(1) = 26, g(2) = 17, g(3) = 22, and

f(6) = 1, f(9) = 3, f(11) = 2.

Assume a 1:1 and onto relationship.  Determine:

a.  fog

b.  gof

9. Given f(w) = 2, f(x) = 5, f(y) = 2, f(z) = 3.  What is the inverse function of 5?  That is, f-1(5) = ?

10.  Assume that the Basis Step for the sum of the first n ODD Integers is n^2.  Develop a table of at least six exs to show this assumption seems to be true.  Hint: Follow the      process used in previous ECRs.

11.  Assume n is a very large value.  List the following elements in ascending order:
 {(n log n^2), 2^n, log 20, 120, log 10, (n^2 log n^2) } 

12.  Define the value of:
PI SIGMA 3*k*j where SIGMA has the range k =0 to 4, and where PI has the range j = 0 to 3.

A. What is the best order to form the product  ABCD if A, B, C  and D are matrices with dimensions  15 x 25, 25 x 30, 30 x 20, and 20 x 15, respectively.  Show your work!  Limit your answer to the four alternatives listed below:   

a)  [( A * B ) * C ] * D     

b)  (A * B ) * ( C * D )      

c)   A * [ B * (C * D ) ]     

d)  [( C * D) * A ] * B     

B. Solve for Computer Time Used when:

Problem size:            n = 10^2
Bit operations used:      n^3 log n
Processor speed:         10^10 operations/sec

Math, Academics

  • Category:- Math
  • Reference No.:- M91433

Have any Question? 

Related Questions in Math

A cooling tower for a nuclear reactor is to be constructed

A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet. The diameter at the base is 260 m and the minimum diameter, 500 m above the base, is 180 m. Find an equation for the ...

A computer retailer requires 100000 hard drives it can

A computer retailer requires 100000 hard drives. It can source these hard drives from company A or company B. Company A's hard drives are cheaper than company B's, but company A's hard drives are defective with probabili ...

1 a suppose that a is a natural number and that a2 is

1. a) Suppose that a is a natural number and that a2 is divisible by 3, show that a is divisible by 3. (Hint: show that if a is not divisible by 3, then neither is a2.) b.) Show that sqrt(3) is not rational.

A country produces only one good it produced 5000 units of

A country produces only one good. It produced 5,000 units of the good during Year 1 and 6,000 units of the good in Year 2. The price of each unit of the good in Year 1 was $280 and it was $320 in Year 2. Suppose Year 1 i ...

1a ladder is leaning against a building the distance from

1.A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 18ft less than the length of the ladder. How high up the side of the building is the top of the ladder if that dista ...

The simple interest i in dollars for a savings account is

The simple interest, I (in dollars), for a savings account is jointly proportional to the product of the time, t (in years), and the principal, P (in dollars). After three months, the interest on a principal of $5000 is ...

The jurassic zoo charges 6 for each adult admission and 3

The Jurassic Zoo charges $6 for each adult admission and $3 for each child. The total bill for the 154 people from a school trip was $558. How many adults and how many children went to the zoo?

How much must you deposit today into an account with annual

How much must you deposit today into an account with annual compounding an a APR of 5% in order to have $25,000 in 8 years

In this question you will build a matrix from the

In this question, you will build a matrix from the eigenvectors and eigenvalues, instead of the other way around. The matrix A has three eigenvalues : λ1=2 with eigenvector u1=(1,1,0), λ2=-3 with eigenvector u2=(1,-1,1)a ...

1 company x will make bags for girls calculate for each bag

1. Company X will make bags for girls. Calculate for each bag the following a) factory overhead for each bag, b) cost of each bag, c) profit margin of each bag and the, d) selling price of each bag. Given the following d ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

A cola-dispensing machine is set to dispense 9 ounces of

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manuf

What is marketingbullwhat is marketing think back to your

What is Marketing? • "What is marketing"? Think back to your impressions before you started this class versus how you

Question -your client david smith runs a small it

QUESTION - Your client, David Smith runs a small IT consulting business specialising in computer software and techno

Inspection of a random sample of 22 aircraft showed that 15

Inspection of a random sample of 22 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise

Effective hrmquestionhow can an effective hrm system help

Effective HRM Question How can an effective HRM system help facilitate the achievement of an organization's strate