Let V be the set of all positive real numbers. Define + by U+V = UV-1 and . by C.V = V. Is V a vector space? Explain?

Answers

Answer 1

No, V is not a vector space with the operations defined in this way. Because the operations defined in this question do not satisfy the properties required for V to be a vector space.

A vector space is a collection of objects (vectors) that can be added together and multiplied ("scaled") by numbers, called scalars. These operations must satisfy certain properties to be considered a vector space.

For example, one of the properties is the associativity of vector addition, which means that (u + v) + w = u + (v + w) for any vectors u, v, and w in V. However, with the given definition of +, we have (U + V) + W = (UV-1) + W = U(VW-1) which is not equal to U + (V + W) = U(VW-1)

Another property is the distributivity of scalar multiplication over vector addition, which means that c(u + v) = cu + cv for any scalar c and any vectors u and v in V. But with the given definition of ., we have C(U+V) = C(UV-1) which is not equal to C.U + C.V = CUV-1

Furthermore, with the definition given the additive identity and the existence of additive inverse are not guaranteed.

Therefore, V is not a vector space with the operations defined in this way.

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Related Questions

2 + − 1 ( − ) + 7 ( 2 − )

Answers

Answer:

Step-by-step explanation:

15

if m2=39 and m3=30 what is m1

Answers

Answer:

m1 = 48

Step-by-step explanation:

this s a sequence of -9

it could only be + square by 3 if shown in question initially as squared m^2 so we cna presume the answer is m = - 9  m1 = 48

Answer:

i cant post the official answer because its "not school related" so i'll post it again :)

Step-by-step explanation:

add 51+18 and you have your answer enjoy :D

Three farmers, share some
bags of fartilizers in the ratio
3:4:5. If the smallest
Share is 18 bags, find the
largest Share

Answers

Your answer is 30 bags, if you do 18/3=6 then 5*6=30

Is 1/3 less than or greater than 5?

Answers

Answer:

Less than

Step-by-step explanation:

not a whole #

What is the first step in solving 5x-2=3

Answers

Answer:

5x-2=3

5x=3+2

5x=5

x=5÷5

x=1

Solve each multi-step equation. Show your work. A - 2 + 3 = -2

Answers

Answer:

a is -3

Step-by-step explanation:

negative 3 minus 2 is negative 5 plus 3 is negative 2

I. 2a + 2b - c + d = -5

II. a + b + d = -2

III. 3a - b + 2c -d = 18

IV. 4b = -c

Hint:

Solve for c first in IV.

Solve for any variable in II next.

Solve I then.

Answers

Answer:

Wat

Step-by-step explanation:

Kind of question is this

sin (3x) dx = ?
find the integral

Answers

Answer:

[tex]\displaystyle \displaystyle \int {sin(3x)} \, dx = \frac{-cos(3x)}{3} + C[/tex]

General Formulas and Concepts:

Calculus

Antiderivatives - Integrals

Integration Constant C

Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Trig Integration: [tex]\displaystyle \int{sin(x)} \, dx = -cos(x) + C[/tex]

U-Substitution

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \int {sin(3x)} \, dx[/tex]

Step 2: Identify Substitution Variables

u = 3x

du = 3dx

Step 3: Integrate

[Integral] Rewrite:                                                                                           [tex]\displaystyle \frac{1}{3}\int {3sin(3x)} \, dx[/tex][Integral] U-Substitution:                                                                                [tex]\displaystyle \frac{1}{3}\int {sin(u)} \, du[/tex][Integral] Trig Integration:                                                                              [tex]\displaystyle \frac{1}{3}[-cos(u)] + C[/tex][Expression] Multiply:                                                                                     [tex]\displaystyle \frac{-cos(u)}{3} + C[/tex][Expression] Back-Substitute:                                                                        [tex]\displaystyle \frac{-cos(3x)}{3} + C[/tex]

Please help me with this ᕕ( ᐛ )ᕗ thank you!

Answers

Answer:

B

Step-by-step explanation:

We can create the equation step-by-step:

Each row of bricks is 6.5cm and the number of row of bricks is r: 6.5r

Total of height of wall: = 259cm

Top row is 1cm shorter: -1cm

Combine all the terms together and we get: 6.5r - 1 = 259

Which means each row of bricks is 6.5cm but minus 1cm from the top to get 259cm the total :D

1.) how much will $5000 be worth in 5 years if it is compounded continuously at 3% interest.

2.) Becky invest $2500 at an annual interest rate of 9%. How much is the investment worth after 10 years if the interest is compounded continuously.

3.) suppose $2000 is invested at 5.75% annual interest compounded continuously for 21 months. How much will the investment be worth at the end of 21 months.


Will mark as Brainlessly or whatever it’s called (if you take my points I will report) thank you so much:)

Answers

Answer:

$5809.17

$6149.01

$2211.72

Step-by-step explanation:

Continous interest formula:

(pv)e^(rt)

we have

5000e^(5*.03)= 5809.17

Same equation from before

2500e^(.09*10)= 6149.01

2000e^(.0575*(21/12))

(we write 21/12 because that's how many years has passed)

= 2211.72

Of the people who fished at Clearwater Park today, 81 had a fishing license, and 9 did not. Of the people who fished at Mountain View Park today, 60 had a license, and 40 did not. (No one fished at both parks.) Suppose that one fisher from each park is chosen at random. What is the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license? Do not round your answer.

Answers

Answer:

9/25 = the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license

Step-by-step explanation:

There are 90 fishers at Clearwater and 100 fishers at Mountain View

The probability of a fisher at Clearwater had a license = 81/90 = 9/10

and the probability of a fisher at Mountain View

did not have a license = 40/100 = 2/5

the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license = 9/10(2/5) = 9/25

The ratio of boys to girls In student council is 4 to 5. Students council has 18 members. How many are boys?

Answers

Answer:

Step-by-step explanation:

boy count is 1476

Explanation:

There is an important difference between the way counts are viewed in ratio to that in fractions.

The ratio of boys : girls

4

:

5

so you have 4 boys and 5 girls making the whole count

4

+

5

=

9

in its simplest form.

So to change the ratio proportion into fraction proportion we have:

boys

4

9

of the whole.

girls

5

9

of the whole.

It is given that the whole is 3321 therefore the count of boys is:

4

9

×

3321

=

1476

A) square root 6

B) 6

C) 6 square root 2

D) 12

E) 12 square root 2

Please help

Answers

sin(45degrees) or BC/AB is 1/sqrt2(that's the value of sin45 degrees I recommend you to memorize this.)

x/12=1/sqrt2

x*sqrt2=12

x=12/sqrt2

Now rationalize this fraction to make the answer more formal.

x=12sqrt2/2(I multiplied both top and bottom by sqrt2)

Now simplify

x=6sqrt2

Question done! answer is C 6 square root of 2

Hope this helped any questions just put them in the comments.

Answer:

6 square root 2

Step-by-step explanation:

How do I Use the order of operations to simplify the expression. 1/3+1/5x1/9

Answers

Answer:

Step-by-step explanation:

1/3+1/5×1/9 = 1/3+1/45 = 9/45+1/45 = 10/45 = 2/9

use multiplication first, multiply 1/5 and 1/9 to get 1/45
then add 1/3,
(multiply 1/3 by 15/15 to get 15/45)

add 15/45 and 1/45 to get 16/45

A 31-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 33 m. Find the length of the shadow. If necessary,
round your answer to the nearest tenth.
B
5
?

Answers

Answer:

Step-by-step explanation:

[tex]\text{By the Pythagorean Theorem the hypotenuse of a right triangle squared is equal to the sum of the squared sides.}\\ \\ h^2=x^2+y^2\\ \\ 33^2=31^2+x^2\\ \\ x^2=33^2-31^2\\ \\ x^2=128\\ \\ x=\sqrt{128}\\ \\ x\approx 11.3m[/tex]

Which variable is most important to the following problem? After two hours, Kaylee measured the temperature of a mixture to be 62.7°F. She noticed it was 3:47 p.m. At 4:58 p.m., the temperature reached its peak at 89.4°F. How much did the temperature of the mixture increase between 3:47 and 4:58?​

Answers

It was the temperature peak 89.4 without this there would be no difference.

Solve. 3 + 4(w + 5) = 31

Answers

Answer:

8/4

We have,

3+4(w+5)

=31 Or, 3+20+4w

=31 or, 4w

=31−23

w=8/4

Thus, w comes out to be 2 .

Step-by-step explanation:

Hope it is helpful....

Answer:

w=2

Step-by-step explanation:

3 + 4(w + 5) = 31

distribute 4(w + 5)

4 x w = 4w

4 x 5 = 20

rewrite your equation

3 + 4w + 20 = 31

add like terms

3 + 20 = 23

rewrite equation

4w + 23 = 31

subract 23 on both sides

4w + 23 = 31

-23 -23

4w = 8

divide by 4 on both sides to get w by itself

4w = 8

4      4

w = 2

Annie plans to purchase a car that will cost her $16,000. After putting down a 20% down payment, how much will Annie need to finance?

Answers

Convert 20% to a decimal by dividing by 100, = 0.20

16,000 x 0.20 = 3,200 deposit she paid. Subtract that from the total cost
16,000- 3,200= 12,800

witch is better gacha life or gacha club or anime or animal crossing ​

Answers

personally i like animal crossing and anime

Answer:

If you want i could make a goup with animal crossing, I also have a anime group but thats at school so i have to cross that out and i dont play gatcha life

Step-by-step explanation:

Which of the I-values are solutions to both of the following inequalities?
81> I and I > 68

Answers

Answer:

Option (C)

Step-by-step explanation:

Given inequalities are,

81 > x and x > 68

Therefore, 81 > x > 68 is the inequality representing the solution area for x.

Out of x = 88, 85 and 80,

x = 80 will lie between the range of x = 68 and x = 81.

Therefore, Option (C) will be the correct option.

PLEASE HELP PLEASEEEE
PLEASE I WILL GIVE YOU COOKIES.

Find the range of the function f(g)=3g-5 for the domain {-2,0,2}


{-9, -4, 5}

{-2, 0, 2}

{ -13, -7, -3}

{-11, -5, 1}

Answers

Answer:

option 4 {-11, -5, 1}

Step-by-step explanation:

range: set of output

f(-2)=3(-2)-5=-11

f(0)=3(0)-5=-5

f(2)=3(2)-5=1

What is the first correct step in solving the inequality-4(3-5x)>-6x+9?

Answers

Answer:

follow PEMDAS (parentheses exponents multiplication division add subtract)

A cup of beans costs N160. How much
would a similar tin, three times the height
and diameter, full of beans cost?​

Answers

Answer:

Below.

Step-by-step explanation:

The volume will be 3^3 = 27 times the volume of the small cup.

Answer is N160 * 27

= N4320.

The cost of a full of beans is N4320 if a cup of beans costs N160 and a similar tin, three times the height and diameter,

What is volume?

It is defined as a three-dimensional space enclosed by an object or thing.

We have:

A cup of beans costs N160.

Cost of volume of a small cup = N160

Let V be the volume of a similar cup

V = 3³ = 27

The cost = 27×160 = N4320

Thus, the cost of a full of beans is N4320 if a cup of beans costs N160 and a similar tin, three times the height and diameter,

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ANSWER QUICKLY PLEASE
Part A
For the following figure, the value of x is

Part B
Using the same figure, determine the value of y.
Choose the suitable option,
A) 16in
B) 64in
C) 8 square root of 2
D) 4 square root of 2

Answers

C Because I Just Guessed You Needa Understand Eaither C Or B Because There in the middle id say c tho

Option C is correct, the value of y is 8 square root of 2.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We need to find the value of y.
The given triangle is right angle triangle with opposite side of 8 inches.

Hypotenuse is y and adjacent side is x.

Now let us solve for sinB

sin45 =8/y

1/√2=8/y

Apply cross multiplication

y=8√2

8 square root of 2

Hence, option C is correct, the value of y is 8 square root of 2.

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In an Arithmetic progression, if d= -4, n=7, an=4, then find a.​

Answers

Answer:

a = 28

Step-by-step explanation:

[tex] a_n = a + (n-1) d[/tex]

[tex] 4 = a + (7-1) (-4)[/tex]

[tex] 4 = a + 6 (-4)[/tex]

[tex] 4 = a - 24[/tex]

[tex] 4 +24= a [/tex]

[tex] a = 28[/tex]

Joe and Jacob are selling pies for a fundraiser. Customers can buy blueberry pies and
apple pies, Joe sold 4 blueberry pies and 7 apple pies for a total of $123. Jacob sold 4
blueberry pies and 2 apple pies for a total of $58. What is the cost of one blueberry pie
and one apple pie.

Answers

Answer:

1234567891011121314151617181920

no entiendo en español menos en ingles

Hello random person and it would be very helpful if you know this answer!

Write the phrase as an expression.

1. 15 decreased by the product of a number x and 4.

Answers

Answer:

4x - 15

hope this helped

The answer is “ 15 - ( X • 4 ) “

arkadaşlar 81×56 kaç​

Answers

Answer:

big

Step-by-step explanation:

pp

Answer:

4536

Step-by-step explanation:

Hesap makinesi kulan

Which one is the correct answer?

Answers

Answer:

3

Step-by-step explanation:

6 (3x+5)=6 (3x)+6 (5)

=18x+30

DISTRIBUTIVE LAW OF ADDITION

Answer:

#3

Step-by-step explanation:

6(3x+5) = 6(3x) + 6(5) = 18x +30

Can I have brainliest please..? hee hee

Help pls!!!!!!!!!!!!!!!!!

Answers

Answer:

the answer is 8/5

Step-by-step explanation:

LCM = 10

(14+2)/10 = 16/10

= 8/5

please give me brainlist if it is helpful for you

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