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
AveGali [126]
3 years ago
5

The given set together with the given operations is not a vector space. list the properties of the definition that fail to hold.

(select all that apply.) the set of all ordered pairs of real numbers with the operations (x, y) ⊕ (x', y') = (x + x', y + y') and r (x, y) = (x, ry).
Mathematics
1 answer:
Triss [41]3 years ago
8 0
Let us look at all the axioms of a vector space and see which axioms are broken. 
1) Associativity<span> of addition
</span>[(1,1)\bigoplus(2,2)]\bigoplus(3,3)=(6,6)
[(1,1)\bigoplus[(2,2)]\bigoplus(3,3)]=(6,6)<span>
It's trivial to see this one holds.
2)</span>Commutativity<span> of addition
</span>(1,1)\bigoplus(2,2)=(2,2)\bigoplus(1,1)=(3,3)
<span>This one holds.
3)</span>Identity element<span> of addition
</span><span>This means that we have zero vektor. It is pretty obvious we do, it is (0,0). 
</span>(a,b)\bigoplus(0,0)=(a,b)
4)Inverse elements<span> of addition
</span>This means that for each element in V there exists element -v such that v+(-v)=0. 
We do have inverse elements.
(a,b)\bigoplus(-a,-b)=(a-a,b-b)=0 
5)Compatibility<span> of scalar multiplication with field multiplication
</span>This one holds.
a[b(c,d)]=ab(c,d)
6)<span>Identity element of scalar multiplication
</span>Identity element of scalar multiplication is simply 1.
1\cdot (a,b)=(a,1\cdot b)=(a,b)
7)Distributivity of scalar multiplication with respect to vector addition. Let's look at the definition.
a[(b,c)\bigoplus(d,e)]=a(b,c)\bigoplus a(d,e)
Now let's look at the example:
a[(1,1)\bigoplus(2,2)]=a(3,3)=(3,3a)
a(1,1)\bigoplus a(2,2)=(1,1a)\bigoplus(2,2a)=(3,3a)
This one hold too.
8)<span>Distributivity of scalar multiplication with respect to field addition
</span>Definition of this one is: 
(a+b)(c,d)=a(c,d)+b(c,d)
Let's take a look at the example:
(3+2)(1,2)=5(1,2)=(1,10)
(3+2)(1,2)=3(1,2)+2(1,2)=(1,6)+(1,4)=(2,10)
So this one doesn't hold.
The final answer would be distributivity of scalar multiplication with respect to field addition.
Please note vectors, in this case, are (a,b) and that I did not use the dot to indicate scalar multiplication.

You might be interested in
PLZ PLZ PLZ HELP ME NOW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
mote1985 [20]

Answer:

red and green

Step-by-step explanation:

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.

4 0
3 years ago
Read 2 more answers
If the coefficient of determination for a data set containing 24 points is 0.5,
aleksandrvk [35]

Answer:

False

Step-by-step explanation:

False - one has nothing to do with the other. None of the data points can lie on the regression line,

and you can have the coeff. of determination be 0.5.

7 0
3 years ago
Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 50 minutes or 0.83¯ hour.<br> Who runs faster?
kenny6666 [7]

Answer:

║⊕║∵°·∵∴Hello :)∴∵·°∵∴║⊕║

Your answer should be:

Maura runs faster.

Step-by-step explanation:

I hope this helped!

<em>Brainliest appreciated</em>

<h2><em>Have a good day!</em></h2>
8 0
3 years ago
emily has saved 75.25 so far for a new phone. the cell phone that she want costs 102.19 How much more money does she need to pur
Alenkinab [10]

Answer:

emily has saved 75.25 so far for a new phone. the cell phone that she want costs 102.19

How much more money does she need to purchase a phone?

The Correct Answer Is $ 26.94

xXxAnimexXx

Have a great day!

6 0
2 years ago
Two sides of a triangle measure 9 cm and 23 cm what could be the measurement of the third side of the triangle
Vladimir79 [104]
Pythagorean Theorem: a^2+b^2=c^2
(9)^2 + b^2 = (23)^2
81 + b^2 = 529
b^2 = 529 - 81
b^2 = 448
b^2 =
\sqrt{448}
b = 21.2
6 0
2 years ago
Other questions:
  • Graph the piecewise function (20 points!)<br> (image provided below)
    10·1 answer
  • An auto transport truck holds 12 cars. A car dealer plans to bring in 1,150 new cars in June and July. If an auto transport truc
    5·1 answer
  • A produce manager needs to order 76 bundles of asparagus for a busy holiday weekend. The supplier received the order, and each o
    7·2 answers
  • Can someone PLEASE help me with questions #5 and 6
    13·1 answer
  • A researcher has collected the following sample data. The mean of the sample below is 5.
    6·1 answer
  • <img src="https://tex.z-dn.net/?f=6%20%3D%20%20%5Cfrac%7Ba%7D%7B4%7D%20%20%2B%202" id="TexFormula1" title="6 = \frac{a}{4} + 2
    9·2 answers
  • 1 − 2 p + 5 = 4 p + 6 what is p in this equation
    9·1 answer
  • Which expression is equivalent to the following complex fraction?
    11·1 answer
  • Which of the following is equivalent to (mn)³?<br><br>a. 3mn<br>b. m³n<br>c. mn³<br>d. m³n³
    12·1 answer
  • Determine which pair of points has a negative slope.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!