Prove that any field IF is also a vector space over itself, with the field addition used as vector addition and the field multiplication used as scalar multiplication.

Answers

Answer 1

We can show that any field IF is a vector space over itself, with the field addition used as vector addition and the field multiplication used as scalar multiplication.

A field is a set of elements, denoted by IF, that satisfies the following axioms:

Commutativity of addition

Associativity of addition

Existence of additive identity

Existence of additive inverse

Commutativity of multiplication

Associativity of multiplication

Distributivity of multiplication over addition

Existence of multiplicative identity

Existence of multiplicative inverse

Given these axioms, we can show that IF is a vector space over itself.

Closure under addition: For any a, b in IF, their sum a + b is also in IF.

Commutativity of vector addition: For any a, b in IF, a + b = b + a.

Associativity of vector addition: For any a, b, c in IF, (a + b) + c = a + (b + c).

Existence of additive identity: The additive identity 0 in the field IF can also be used as the additive identity in the vector space.

Existence of additive inverse: For any a in IF, its additive inverse -a in the field IF can also be used as the additive inverse in the vector space.

Distributivity of scalar multiplication over vector addition: For any a in IF and any u, v in IF, a * (u + v) = a * u + a * v.

Distributivity of scalar multiplication over field addition: For any a, b in IF and any u in IF, (a + b) * u = a * u + b * u.

Existence of multiplicative identity: The multiplicative identity 1 in the field IF can also be used as the multiplicative identity in the vector space.

Therefore, we have shown that any field IF is a vector space over itself, with the field addition used as vector addition and the field multiplication used as scalar multiplication.

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Related Questions

Write the equation of the line with y-intercept 3 and a slope of – 2/3

Answers

Answer:

y = -2/3x + 3

Step-by-step explanation:

The slope intercept form of the equation of a line is

y = mx+b where m is the slope and b is the y intercept

y = -2/3x + 3

Answer:

\(y = - \frac{2}{3} x + 3\)

Step-by-step explanation:

\(y = mx + b\)

where y us unknown, m is -2/3 and b is 3

How do I solve this question

How do I solve this question

Answers

Then to find y you would do
3y+1+56=180
3y+57-57=180-57
3y/3=123/3
Y=41
How do I solve this question

What is the value of S4 for
0 554
O
64
O
(J1
14
O 516
05/0
O
56
n-1
24 (1)
n=1
?

What is the value of S4 for0 554O64O(J114O 51605/0O56n-124 (1)n=1?

Answers

Answer:    It's not entirely clear what is being asked for in the given question, as it is not clear what the numbers represent or what operation is being performed. If you could provide more information or context, I would be happy to try and help you.

Step-by-step explanation:

what is the y-intercept of the line shown below?

A:3/4
B:2
C:3
D:4​

what is the y-intercept of the line shown below?A:3/4B:2C:3D:4

Answers

The y-intercept is the y value where the blue line crosses the Y axis which is the vertical black line.

The line crosses at the number 4, so the y-intercept is 4

Answer: D. 4

2. Which of the following represents the
center of dilation?
3.51
3
2.5
2.
1.5
(1, 1.5
1
1
A
0.5
(3,1)
0.5, 0.5) (1.5, 0.5)
.
ov
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
A. (0,0)
B. (1,6)
C. (3,1)
D. (2,3)

2. Which of the following represents thecenter of dilation?3.5132.52.1.5(1, 1.511A0.5(3,1)0.5, 0.5) (1.5,

Answers

Answer:

B (1,6)

Step-by-step explanation:

I don't know if I'm right

2. The size of garage after a 12% decrease is 150 square feet. What was the original
size of the garage? Round to the nearest whole feet.

Answers

Answer:

168ft^2

Step-by-step explanation:

150 · 0.12 = 18.

150 + 18= 168

George buys a computer. He pays a deposit of $200 and six monthly instalments of $55.

How much does George pay for his computer in total?

Answers

The total amount that George pays for his computer after making an initial deposit (down payment) of $200 and six monthly installments of $55 is $530.

What is the down payment?

The down payment refers to the advance cash payment that retailers demand from potential customers for the purchase of an item on credit.

The down payment is also referred to as an initial deposit or cash advance.

Making the required down payment assures the retailer of the buyer's financial credibility, ability, and willingness to undertake the credit transaction.

The initial deposit made by George = $200

The monthly installments = $55

The installment period = 6 months

The total installment payments = $330 ($55 x 6)

The total payment for the computer = $530 ($200 + $330)

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x=4y-7
2x+9y=-31
What be the answer

Answers

Answer:

x=-11

y=-1

Step-by-step explanation:

x=4y-7

2x+9y=-31

2(4y-7)+9y=-31

8y-14+9y=-31

17=-31+14

17y=-17

y=-1

x=4(-1)-7

x=-11

Answer:

x = -11, y = -1

Step-by-step explanation:

solving simultaneously,

2(4y-7) + 9y = -31

17y = 14 - 31

17y = -17

y = -1

back sub, we get:

x = 4(-1)-7

x = -11

so x = -11, y = -1

solve by elimination
(show all your work)
14x = 2y + 16
5x = y + 2

Answers

Answer:

x=3

y=13

Step-by-step explanation:

Multiply the second equation by 2:

2(5x=y+2) = (10x=2y+4)

Subtract one equation from the other:

   14x=2y+16

-   10x=2y+4

=  4x=12

Solve for x:

4x=12

x=3

Solve for y by plugging in x:

5(3)=y+2

15=y+2

13=y

a. Find the slope of x^3+y^3-65xy=0 at the points (4,16) and (16,4).
b. At what point other than the origin does the curve have a horizontal tangent​ line?
c. Find the coordinates of the point other than the origin where the curve has a vertical tangent line.

a. Find the slope of x^3+y^3-65xy=0 at the points (4,16) and (16,4).b. At what point other than the origin

Answers

a. The  slope of the curve at the point (4,16)   is approximately 1.165, and at the point (16,4)  is approximately -0.496.

b. The   curve has a horizontal tangent line at the points(0,0) and (3,27).

c. The   curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).

How is this so?

a. To find the   slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.

Differentiating the equation with respect to x, we have  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.

For the point (4,16)  -

3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0

48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0

508(dy/dx) = 592

(dy/dx) = 592/508

(dy/dx) ≈ 1.165

For the point (16,4)  -

3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0

768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0

(-992)(dy/dx) = 492

(dy/dx) = 492/(-992)

(dy/dx) ≈ -0.496

Thus, the slope of the   curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.

b. To find the point where the curve has   a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.

This means   the slope is zero and the tangent line is horizontal.

From the derivative we obtained earlier  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

Setting dy/dx equal to zero  -

3x² - 65y = 0

Substituting y = x³/65 into the equation  -

3x² - 65(x³/65) = 0

3x² - x³ = 0

Factoring out an x²  -

x²(3 - x) = 0

This equation has two solutions  -  x = 0 and x = 3.

hence, the curve has a horizontal   tangent line at the points(0,0) and (3,27).

c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s)   where the derivative is undefinedor approaches infinity.

From the derivative  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.

Setting the denominator equal to zero:  -

65x = 65y

x = y

Substituting this condition back into the original equation  -

x³ + x³ - 65x² = 0

2x³ - 65x² = 0

x²(2x - 65) = 0

This equation has two solutions  - x = 0 and x = 65/2.

Therefore, the curve has a vertical tangent line   at the points (0,0)

and(65/2, (65/2)³).

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In the diagram, all measurements are in centimetres.
ABC is an isosceles triangle.
AB - 2x
AC - 2x
BC - 10
(a) Find an expression, in terms of x, for the perimeter of the triangle
Simplify your expression.
(2)
The perimeter of the triangle is 34 cm.
(b) Find the value of x.

Answers

Answer:

y = 4x + 10         x = 6

Step-by-step explanation:

a)  perimeter = 2x + 2x + 10 = 4x + 10

b)  perimeter = 34

⇒ 4x + 10 = 34

⇒ 4x = 34 - 10 = 24

⇒ x = 24 ÷ 4 = 6

I need to know how to solve this equation

I need to know how to solve this equation

Answers

Answer:

D

Step-by-step explanation:

a

--- + 8 = 4

-2.1

a

---- =4 - 8

-2.1

a

--- = -4

-2.1

a= -4 × -2.1

a= 8,4

the answer is D! hopefully this helps
I need to know how to solve this equation

. The table below shows the cost of making a long distance call based on the length of the call. Long Distance Rates Time (minutes) Cost 5 $0.55 6 $0.62 7 $0.69 8 $0.76 9 $0.83 10 $0.90 Refer to the above table of long distance rates. Write an expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes.

Answers

An expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes is (0.55 + (n - 5) x 0.07) dollars.

Given:

Long Distance Rates Time (minutes) Cost5 $0.556 $0.627 $0.698 $0.769 $0.8310 $0.90We need to find an expression that can be used to find the cost of an n-minute long-distance call, where n is at least 5 minutes.

The cost of making a long-distance call is given for 5 minutes, 6 minutes, 7 minutes, 8 minutes, 9 minutes, and 10 minutes.

We can observe from the above table that for every increase of 1 minute, the cost increases by $0.07.

We can conclude that the cost of n minutes long-distance call is given by: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes.

Therefore, the required expression is: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes. The above expression is based on the pattern in the table provided for long-distance call rates. We can use this expression for values of n greater than or equal to 5.

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For the past 6 years, a town has held a festival in June. The first year it was held, only 200 people attended. Last year, 814 people attended. Let p represent the number of people who attended any other year. If attendance for the festival has increased every year, which inequality best describes the value of p? A. 200 < p > 814 B. 200 < p < 814 C. 200 > p > 814 D. 200 > p < 814 ​

Answers

The inequality that best describes the value of p is A. 200 < p > 814.

What is an inequality?

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let p represent the number of people who attended any other year.

Since there's always an increase, the inequality will be 200 < p > 814.

The correct option is A.

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casey is using statistical techniques to examine whether children with autism differ in the amount of self-esteem they report as compared to children without autism. she finds a significant difference, which suggests that the results of her analysis

Answers

Casey's analysis suggests that her hypothesis was correct - children with autism have lower self-esteem than children without autism.

Casey's analysis is that children with autism have lower self-esteem than children without autism. To reach this conclusion, Casey first needed to design an experiment in which she could accurately measure the self-esteem of both groups.

She then collected data from her experiment and applied statistical techniques to compare the two groups. Finally, she found a statistically significant difference between the two groups, meaning that the difference was unlikely due to chance alone.

This result suggests that her hypothesis was correct - children with autism have lower self-esteem than children without autism.

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Calculate the circumference of this circle π3.14 radius= 36 in

Answers

Answer:

C≈226.19in

#carryonlearning

(XA) 26. In a certain community, 65% people speak Newar language and 45% people speak Gurung language. Find percentage of people who can speak (i) both the languages. (ii) Newari only (iii) Gurung language only.​

Answers

Answer: (i) 10% (ii) 60% (iii) 40%

Step-by-step explanation:

(i)  Newar language = 65%

  Gurung language = 45%

Total covers = 110 but to sum it up to base that is 100% then 110-100 is 10.

so, 10% of people speak both the language.

(ii) people who speak only Newari only would be 60% as 5% among them speak Gurung language.

(iii) people who speak only Gurung only would be 40% as 5% among them speak Newari language.

Question 21
< >
In a large population, 60% of the people have been vaccinated. If 3 people are randomly selected, what is
the probability that at least one of them has been vaccinated?
Give your answer as a decimal to 4 places.
Question Help: Message instructor
Submit Question
4

Answers

Answer: 0.9360

Step-by-step explanation: To find the probability that at least one of the three people has been vaccinated, we need to find the probability that none of them have been vaccinated and then subtract that from 1.

The probability that a person has not been vaccinated is 1 - 0.6 = 0.4. Therefore, the probability that all three people have not been vaccinated is:

P(no one vaccinated) = 0.4 × 0.4 × 0.4 = 0.064

So, the probability that at least one of the three people has been vaccinated is:

P(at least one vaccinated) = 1 - P(no one vaccinated) = 1 - 0.064 = 0.936

Therefore, the probability that at least one of the three people has been vaccinated is 0.936 (to 4 decimal places).

Answer: 0.9360

Which statement is true about the equations -3x + 4y = 12 and 1/4x-1/3y= 1?
The system of the equations has exactly one solution at (-8, 3).
The system of the equations has exactly one solution at (-4, 3).
The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.

Answers

Answer:

the third selection is corret

Step-by-step explanation:

Ax + by + c = 0, k = - a/b.

so The slope of the first line = \(\frac{4}{3}\),

the slope of the second line = \(\frac{4}{3}\);

So these two lines are parallel and they don't intersect

Rick Rich owns a Mercedes dealership. Mercedes has 5 models, 4 standard options packages, and 5 colors. If Rick wants to immediately be able to deliver any car (model, option package, color), how many cars must Rick have on hand?

Answers

Rick would need to have at least 100 cars on hand to immediately be able to deliver any car (model, option package, color).

To immediately deliver any car, Rick Rich's dealership must have all possible combinations of Mercedes models, option packages, and colors in stock.

With five models, four option packages, and five colors, there are 5 x 4 x 5 = 100 possible combinations.

Therefore, Rick would need to have at least 100 cars on hand, each representing a unique combination of model, option package, and color. It's worth noting that having exactly 100 cars on hand would only allow Rick to deliver one of each possible combination, so it may be prudent to have additional inventory on hand to meet demand for more popular combinations.

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Assuming that a local cost cutter provides cuts perms and hair styling service and you fix cost are $120,000 in the variable cost or 40% of the sales revenue last year’s revenue total of $250,000. What is the break even points in sales dollars?

Answers

Answer:

Unit selling price

$7 $9 $7

Unit variable costs

(4) (5) (1)

Unit contribution margin

$3, $4, $6

With monthly fixed costs of $306,000, the company sells two units of A for each unit of B and three units of B for each unit of C.

In ΔMQN, m b. Find the measure of <2. Show all work.

Answers

Answer:

Answer:

131°

Step-by-step explanation:

Since KNJ is a straight line,

∡KNM +∡MNJ= 180° (adj. ∡s on a str. line)

(8x -5)° +(4x -19)°= 180°

Simplify:

12x -24= 180

+24 on both sides:

12x= 180 +24

12x= 204

Divide both sides by 12:

x= 204 ÷12

x= 17

∡KNM

= (8x -5)°

= [8(17) -5]°

= (136 -5)°

= 131°

Darren and barb each tried to evaluate 6(2) + 4 ÷ 2 who elaluated the expression correctly?

Answers

Answer:

14

Step-by-step explanation:

6(2)

12

4÷2

2

12+2

pemdas

Answer:

14

Step-by-step explanation:

first u multiply 6 and 2 to get 12 because u always start with parenthesis or squares, then you divide 4 and 2 to get 2 because afterwards u play around with the multiplication and division. finally u add both answers u got to get 14

really need help with is problem if any math wizards are on

really need help with is problem if any math wizards are on

Answers

Answer:

2

DNE

-3

3

Step-by-step explanation:

(1) DNE because it is not continuous

(2) DNE because it is not continuous

(3) -3 because at 4, f(x) = -3

(4) x can be any value of -5-2k (where k is a positive integer) or 3. So you can just put 3.

A glass of lemonade took 2 1/2 scoops of sugar to make in it. If you wanted to make 3 glasses how many scoops of sugar would you need

Answers

\(\huge\color{yellow}\boxed{Question}\)

A glass of lemonade took 2 1/2 scoops of sugar to make in it. If you wanted to make 3 glasses how many scoops of sugar would you need

\(\huge\color{red}\boxed{Answer}\)

First,Change the fraction to decimal. 2½=2.5Second,Simply Multiply it by 3! 2.5×3=7.5

Therefore, you need 7.5 (7½) scoop of sugar to make 3 glasses of lemonade.

Can someone please help me solve this? I have no idea how to solve

Can someone please help me solve this? I have no idea how to solve

Answers

Answer:

Step-by-step explanation:

I hope this helps

Can someone please help me solve this? I have no idea how to solve

PLEASE HELP WILL GIVE BRAINLIEST IF HELPFUL.

log base (2) of (x^2 +5) = (3)

Answers

Answer:

x=-√3, √3

Step-by-step explanation:

log base (2) of (x^2 +5) = (3)  ==> log base (2) of (x^2 +5) -> 2^(?)=x^2 +5

2^(log base (2) of (x^2 +5)) = 2^(3)  ==> important step

2^(log base (2) of (x^2 +5)) = 8

x^2+5 = 8

x^2+5-5=8-5

x^2=3

x=-√3, √3

The sum of two numbers is −45. One number is 9 more than the other. Find the numbers

Answers

Answer:

-18 and -27 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

ONE OF THE COLDEST TEMPERTURES EVER RECORDED WAS -128F IN ANTARCTICA. ONE OF THE WARMEST TEMPERATURES EVER RECORDED WAS 134 DEGREES FAHRENHEIT IN DEATH VALLET CALIFORNIA. HOW MANY DEGRESS DIFFERENCE ARE THERE BETWEEN THE COLDEST AND WARMEST RECORDED OUTSIDE TEMPERTURE

Answers

Answer:

271 degrees

Step-by-step explanation:

143-(-128)=143+128=271 degrees

Is the following number rational or irrational?
Pi/5
Choose 1 answer:
Rational
B
Irrational

Is the following number rational or irrational?Pi/5Choose 1 answer:RationalBIrrational

Answers

it would be irrational
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