1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Maurinko [17]
3 years ago
12

Let H be the set of all points of the form ​(s,sminus​1). Determine whether H is a vector space. If it is not a vector​ space, d

etermine which of the following properties it fails to satisfy. 1. Contains a zero vector 2. Closed under vector addition 3. Closed under multiplication by scalars A. H is not a vector space because it does not contain a zero vector. B. H is a vector space. C. H is not a vector space because fails to satisfy all three properties. D. H is not a vector space because it is not closed under vector addition.
Mathematics
1 answer:
Sever21 [200]3 years ago
5 0

Answer:

Question Details:

Solve the problem.

Let H be the set of all points of the form (s, s-1). Determinewhether H is a vector space. If it is not a vector space, determinewhich of the following properties it fails to satisfy.

LET ANY 2 VECTORS IN H BE U=[A,A-1] AND V=[B,B-1]

LET K BE ANY SCALAR

A: Contains zero vector

LET THE ZERO VECTOR BE [Z,Z-1].

THEN WE SHOULD HAVE

A+Z=A ....THAT IS

[A+Z,A+Z-2]=[A,A-1]

HENCE A=A+Z....Z=0

A+Z-2=A-1....Z=1...CONTRADICTORY

SO NO ZERO ELEMENT EXISTS.

B: Closed under vector addition

A+B=[A,A-1]+[B,B-1]=[A+B,A+B-2]....NOT AN ELEMENT OF H AS IICOORDINATE SHOULD BE A+B-1.

SO NOT CLOSED IN ADDITION.

C: Closed under multiplication by scalars

K[A,A-1] =[KA,KA-K].......NOT AN ELEMENT OF H AS II COORDINATESHOULD BE KA-1.

SO NOT CLOSED IN SCALAR MULTIPLICATION.

Student Response

Percent              Correct                  Student                 Answer

Value                Response  Response               Choices

 

0.0%                                                             H is not a vector space;

                                                                                 does not                                      

                                                                                 contain zero vector

             

0.0%                                                                       b.H is a vector space.

                                     

0.0%                                                                 c. H is not a vector space;  

                                                                                   not closed under    

                                                                                      vector addition

                                                                                 

 

100.0%                                                             d. H is not a vector  space

                                                           ; fails to satisfy all three  properties

                                                                         

                                 

                                                             

AS YOU CAN SEE ABOVE H IS NOT A VECTOR SPACE .

IT FAILED TO SATISFY THE ABOVE 3 PROPERTIES.

PLEASE NOTE THAT FAILURE TO SATISFY EVEN A SINGLE PROPERTY

IS ENOUGH TO RULE IT OUT AS A VECTOR SPACE

You might be interested in
Algebra 2. Please help! I got 40% on my last try
bixtya [17]
Maybe third one ( -2 -8)
3 0
2 years ago
Read 2 more answers
Giving brainlest Help Please
iragen [17]

Answer:

1.6cm:

Step-by-step explanation:

1cm = 2m

2 divided by 1 = 2

3.2 divided by 2 =1.6

1.6cm

7 0
2 years ago
Barbara has a goal to read 45 minutes every day.
Natali5045456 [20]

First analyze your question. Barbara has a goal to read 45 minutes every day. If she meets her goal, how many minutes will she have read in 360 days?
So....
360*45=16,200

The answer is D. 16,200

Good luck with your studies, I hope this helps!!

8 0
3 years ago
I need help in Kahn academy
Alex17521 [72]

Please post your question.

4 0
3 years ago
Read 2 more answers
Three friends pay $1,025 to rent a vacation home. Beth contributed $80 more than Danny. Katie contributed $20 less than Beth. Ho
lord [1]

Answer:

  $295

Step-by-step explanation:

Let d represent the amount Danny contributed. Then Beth contributed (d+80) and Katie contributed ((d+80)-20) = (d+60). The total from the three friends is ...

  d + (d+80) +(d+60) = $1025

  3d = 885 . . . . . . . . . . . . . . . . . . . subtract 140

  d = 295 . . . . . . . . . . . . . . . . . . . . divide by 3; Danny's contribution

Danny contributed $295.

4 0
3 years ago
Other questions:
  • I need a this for tomorrow. To confusing
    10·1 answer
  • Help! Need #14 plz show work
    8·1 answer
  • 5=-1(4)x+b<br> I need the help pleasee and thank youu!!
    14·1 answer
  • M=2*2*3*5*5 and N=2*2*2*3*3*7 find the largest number that divides exactly M and N​
    11·1 answer
  • PLEASE HELPPPP!!!!! need help with this
    5·1 answer
  • Fiona started her study of bacteria growth with 1,000 bacteria in a petri dish. After 1 hour, the count was increased to 1,800.
    7·2 answers
  • A.<br> X - y = 3<br> 2x - 4y = 8<br> Given ordered pair: (2,-1).
    12·1 answer
  • Plz help me asap i need help plz i will mark you as brainlist
    12·1 answer
  • How many learners can enrol if there are 12 teachers and a ratio of teachers to learners is 30:1
    12·1 answer
  • Anyone 100% kno dis it’s for a test
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!