Let L: V → W be a linear mapping, and let B = {61,..., bn} be a spanning set for V. Prove that C = {L(6),..., L(in)} is a spanning set for Range(L).

Answers

Answer 1

The set C = {L(6), ..., L(in)} spans the range of the linear mapping L because each vector in the range can be expressed as a linear combination of vectors in C.

To prove that C = {L(6), ..., L(in)} is a spanning set for the range of L, we need to show that every vector in the range of L can be written as a linear combination of vectors in C.

Let v be an arbitrary vector in the range of L. By the definition of the range, there exists a vector u in V such that L(u) = v. Since B = {61, ..., bn} is a spanning set for V, we can express u as a linear combination of vectors in B: u = a1 * 61 + a2 * 62 + ... + an * bn, where a1, a2, ..., an are scalars.

Now, applying L to both sides of the equation, we have L(u) = L(a1 * 61 + a2 * 62 + ... + an * bn). Using the linearity of L, we get v = a1 * L(61) + a2 * L(62) + ... + an * L(bn). This shows that v can be expressed as a linear combination of vectors in C. Since v was an arbitrary vector in the range of L, we conclude that C = {L(6), ..., L(in)} spans the range of L.

LEARN MORE ABOUT vector here: brainly.com/question/31265178

#SPJ11


Related Questions

Someone help me please!

Someone help me please!

Answers

Answer:

A: the scale is missing



i hope this helps

Step-by-step explanation:

Answer:

the numbers are supposed to start at zero and the scale is missing

Please solve with explanation! 20 points and will give brainliest

Answers

Answer:

solve what? there is no question or anything attached

Step-by-step explanation:

Solution:

You can attach a file or a picture to show us the question.

where are the ceros located in f(x)=x^4-3x^3-2x^2+3x-5

Answers

Answer:

Zeroes: (-1.45, 0) and (3.45, 0)

Step-by-step explanation:

I plugged the equation into a graphing calc and located the x-values when graphing.

Please answer CORRECTLY !!!!! Will mark brainliest !!!!!!!

Please answer CORRECTLY !!!!! Will mark brainliest !!!!!!!

Answers

Answer:

Width: 2x+1

Step-by-step explanation:

59 out of 95 students are going on a field trip. What is the ratio of the number of students who are staying at school to the number of students who are going on the field trip?

Answers

Answer:59:95

Step-by-step explanation:

Why it is very important to follow the steps in solving an equation with 2 or more operations involve?

Answers

Yeah but I said the answer is yes because of the color

how do you find the z score if you are given the p-value?

Answers

Answer:

la caca eres tu

Step-by-step explanation:

Gracias pinche vaca

The math department needs to buy new textbooks and laptops for the computer science classroom. The textbooks cost $116.00 each, and the laptops cost $439.00 each. If the math department has $6500 to spend and purchases 30 textbooks, how many laptops can they buy?
1) 6
2) 7
3) 11
4)12

Answers

Answer:

1) 6 (the answer is 6)

Step-by-step explanation:

First, let's calculate how much the textbooks cost in total: 30 textbooks * $116.00/textbook = $<<30*116=3480.00>>3480.00

Then, let's subtract the cost of the textbooks from the total amount of money the math department has available: $6500.00 - $3480.00 = $<<6500-3480=3015.00>>3015.00

Finally, we can divide the amount of money the math department has left by the cost of each laptop to determine how many laptops they can afford: $3015.00 / $439.00/laptop = 6.83 laptops

Since it's not possible to buy a fraction of a laptop, the math department can only buy 6 laptops. Therefore, the answer is 6, which corresponds to choice (1).

At any time t > 0,the rate at which a person can memorize a list of M words is proportional to the product of the number of words memorized ad tlie number of words tlat have not been memorized. If 2 denotes the number of words memorized at time t, which differential equation models this situation? Assume kis a positive constant; A. d k dt B. d k ( - M) dt C d k(M - 2) dt D. d =Rt(M -t) dt

Answers

The differential equation that models this situation is dx/dt = kx(M - x) (option c).

To determine the differential equation that models the situation, let's analyze the problem statement.

The rate at which a person can memorize a list of M words is proportional to the product of the number of words memorized and the number of words that have not been memorized.

Let's denote the number of words memorized as "a" and the number of words not yet memorized as "M - a" (where M is the total number of words in the list).

The problem states that the rate of memorization is proportional to the product of "a" and "M - a". We can express this mathematically as:

Rate of memorization ∝ a * (M - a)

To convert this proportionality into an equation, we introduce a positive constant k:

Rate of memorization = k * a * (M - a)

The left side of the equation represents the rate of change of the number of words memorized (da/dt), and the right side represents the product of "a" and "M - a" multiplied by the constant k.

Therefore, the differential equation that models this situation is:

da/dt = k * a * (M - a)

Comparing this with the given options, we can see that the correct choice is option C:

dx/dt = k * x * (M - x)

The complete question is:

At any time t > 0 the rate at which a person can memorize a list of M words is proportional to the product of the number of words memorized and the number of words that have not been memorized. If a denotes the number of words memorized at time t, which differential equation models this situation? Assume k is a positive constant.

A. dx/dt = kx

B. dx/dt = kx(x - M)

C. dx/dt = kx(M - x)

D. dx/dt = kt(M - t)

To know more about differential equation:

https://brainly.com/question/32524608


#SPJ4

-2 3/7 - 1 2/3 show ur work!please

Answers

Answer:

-4 2/21

Step-by-step explanation:

-2 3/7 - 1 2/3

Change to improper fraction

-2 3/7 = -17/7

- 1 2/3 =-5/3

-17/7-5/3

L.C.M=21

-51-35/21

= -86/21

= -4 2/21

Hope it helps..

Please mark brainliest

9. sonja is cutting wire to construct a mobile. she cuts 100 inches for the first piece, 80 inches for the second piece. and 64 inches for the third piece. assuming the pattern continues, write an explicit formula for the nth piece. sonja only has 40 feet of wire to use for the project and wants to cut 20 pieces total for the mobile using her pattern. will she have enough wire? justify your answer.

Answers

Total length of wire = 8.33 + 6.67 + 5.33 + ...20 terms= 100[2 - 0.8^20] / [1.2]≈ 80.99 feet Since the total length of wire required is less than the available wire, Sonja will have enough wire.

Given, Sonja cuts 100 inches for the first piece, 80 inches for the second piece, and 64 inches for the third piece. We need to find the explicit formula for the nth piece.We can see that Sonja is cutting wire in decreasing order of 20%.So, the explicit formula for the nth piece can be given by an = a1 * r^(n-1)where a1 = 100 and r = 0.8 Thus, the explicit formula for the nth piece can be given byan = 100 * (0.8)^(n-1)Now, we need to find if Sonja has enough wire for the mobile as she only has 40 feet of wire to use for the project and wants to cut 20 pieces total for the mobile using her pattern.We know that 1 inch = 0.0833 feet 100 inches = 100 * 0.0833 feet = 8.33 feet80 inches = 80 * 0.0833 feet = 6.67 feet64 inches = 64 * 0.0833 feet = 5.33 feet Now, we can find the total length of wire Sonja needs to cut 20 pieces. Therefore, she can complete the mobile using the given pattern.

for more search question length

https://brainly.com/question/28108430

#SPJ8

Explain carefully and succinctly why, in the execution of the Simplex Algorithm, a variable which is extracted from the basis can NEVER re-enter the basis at the VERY next step.

Answers

Execution of the Simplex Algorithm

In the execution of the Simplex Algorithm, a variable that is extracted from the basis can never re-enter the basis at the very next step due to the optimality conditions and pivoting operations. Here's a step-by-step explanation:

1. Simplex Algorithm is an iterative method for solving linear programming problems.
2. The algorithm starts with an initial feasible solution (basis) and searches for an improved solution by changing the basis (swapping non-basic and basic variables).
3. At each iteration, the algorithm selects a non-basic variable to enter the basis (entering variable) and a basic variable to leave the basis (leaving variable). This is done by pivoting on the element corresponding to the entering and leaving variables in the tableau.
4. The pivot operation enforces that the objective function value improves in each step by increasing (maximization problem) or decreasing (minimization problem) the value of the entering variable.
5. After the pivot operation, the new solution is still feasible, and the entering variable becomes part of the basis while the leaving variable becomes non-basic.
6. The algorithm terminates when no more improvement in the objective function value is possible, meaning that an optimal solution has been found or the problem is unbounded.

Since the entering variable is chosen to improve the objective function, and the pivot operation enforces an improvement, the variable that has just left the basis cannot re-enter at the very next step. If it were to re-enter, it would negate the improvement achieved in the previous step, violating the optimality conditions of the Simplex Algorithm.

#SPJ11

A rectangle is shown. The length of the rectangle is labeled 10 feet. The width of the rectangle is labeled 4 feet.

What are the dimensions if the poster is enlarged by a factor of three over two?

A. 12ft by 30ft
B. 2ft by 5ft
C.6ft by 15ft
D.5ft by 12ft

Answers

Answer:

C, 6 by 15 ft.

Step-by-step explanation:

10*3/2=15, and 4*3/2=6, so we get 6 by 15ft

Pls brainliest for leveling up

⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️

Answers

Answer: lol why so expensive.

Point J (-1,4) is reflected over the line y = 2. What is the coordinates for J’?

Answers

Answer:

(-1, -4)

Step-by-step explanation:

Make the y value the opposite value.

help is appreciated
(ANY LINKS OR WEBSITES WILL BE REPORTED)


:) will give brainliest

 help is appreciated (ANY LINKS OR WEBSITES WILL BE REPORTED) :) will give brainliest

Answers

Answer:

95/9

Step-by-step explanation:

It will be easier for us to make the mixed numbers fractions.

2 1/3 = 7/3

8 2/9 = 74/9

now we want them to have the same denominator so we multiply the 7/3 fraction by 3/3.

21/9 + 74/9 = 95/9

ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°, what is the value of m?
6
17
90
102

Answers

Answer:

The correct answer is option B.  17

Step-by-step explanation:

It is given that, ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°

To find the value of m

From the figure we can see that, triangle WYZ is an isosceles  triangle.

ZW = ZY

Then <YXZ = <WXZ = 90°

It is given ∠YXZ  = (6m – 12)°

(6m – 12)° =  90°

6m = 90 + 12  = 102

m = 102/6 = 17

Therefore the value of m = 17

The correct answer is option B.  17

Answer:

its 17. so B

Step-by-step explanation:

just did it

PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS

PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS

Answers

Answer:

(2,4)

Step-by-step explanation:

hope this helps!

solve for x 4(−7x−2)−10=-3 + 5x+1

Answers

Answer:

i think the answer is -33

Step-by-step explanation:

Module 8: Homework 2 - Confidence Intervals (Mean) Score: 2/4 2/4 answered Question 3 > The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 50.9 for a sample of size 30 and standard deviation 18.7. Estimate how much the drug will lower a typical patients systolic blood pressure (using a 90% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.

Answers

The drug is estimated to lower a typical patient's systolic blood pressure by at least -56.367 and at most -45.433 (using a 90% confidence level).

To estimate the reduction in systolic blood pressure with a 90% confidence level, we can construct a confidence interval using the sample mean and standard deviation. Since the sample size is 30 and the data is assumed to be normally distributed, we can use the t-distribution.

The formula for a confidence interval for the mean is:

CI = Mean ± t * (s / √n),

where mean is the sample mean, s is the sample standard deviation, n is the sample size, and t is the critical value from the t-distribution corresponding to the desired confidence level.

In this case, the sample mean (x) is 50.9, the sample standard deviation (s) is 18.7, and the sample size (n) is 30. Since we want a 90% confidence level, we need to find the critical value (t) with a degree of freedom of 29 (n-1) and a tail probability of 0.05 (1 - 0.90).

Using statistical tables or software, we find that the critical value is approximately 1.699.

Plugging in the values, we can calculate the confidence interval:

CI = 50.9 ± 1.699 * (18.7 / √30).

Calculating the interval, we get:

CI = 50.9 ± 9.968.

Simplifying, we have:

CI = (-58.868, -42.932).

Therefore, the drug is estimated to lower a typical patient's systolic blood pressure by at least -56.367 (rounded to three decimal places) and at most -45.433 (rounded to three decimal places) with a 90% confidence level.

To know more about confidence level refer here:
https://brainly.com/question/22851322#

#SPJ11

Which system of equations has a solution of (-2,-2,-2)?
OA
s+y=0
3-==-2
s+y=z=-4
OB. 31 - y = -8
y - 3z = -8
2 + y + z = -8
OC.
1 + 2y = -6
y + 2z = -6
I-y-z = 2
OD. 1-2y + z = 0
2y +9z = -20
I= y + z = 0

Answers

The system of equations that have a solution of (-2,-2,-2) is (b) x + 2y = -6, y + 2z = -6 and x - y - z = 2

How to determine the system of equations?

The attached figure represents the proper format of the equations.

The solution is given as:

(x,y,z) = (-2,-2,-2)

To determine the system of equation, we simply substitute the values of x, y and z in the equations in the options.

So, we have:

Option 1:

x + y = 0

y - z = -2

x + y - z = -4

Evaluate

x + y = 0

-2 - 2 = 0 --- False

This means that this system of equations do not have a solution of (-2,-2,-2)

Option 2:

x + 2y = -6

y + 2z = -6

x - y - z = 2

Evaluate

x + 2y = -6

-2 + 2 * -2 = -6 --- True

y + 2z = -6

-2 + 2 * -2 = -6 ---- True

x - y - z = -2

-2 + 2 + 2 = 2

This means that this system of equations have a solution of (-2,-2,-2)

Read more about system of equations at:

https://brainly.com/question/14323743

#SPJ1

Which system of equations has a solution of (-2,-2,-2)?OAs+y=03-==-2s+y=z=-4OB. 31 - y = -8y - 3z = -82

In a mixture of 60 litres, the ratio of milk to water is 2:1. If this ratio is to be 1:2,then find the quantity of water to be further added.

Answers

Answer:

Quantity of milk = 60 x 2/3 litres = 40 litres.

Quantity of water in it = (60- 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres.

Then, milk : water = 40 /20 + x

Now, 40 /20 + x = 1/2

20 + x = 80

x = 60.

Quantity of water to be added = 60 litres.

Can someone answer this asap #needhelp thanks

Can someone answer this asap #needhelp thanks

Answers

Answer:i think it is 7/3

Step-by-step explanation:

Pls help I need a lot ive failed this 3 times I can't fail again ahhh please help​

Pls help I need a lot ive failed this 3 times I can't fail again ahhh please help

Answers

Did you right the wrong answers

Help me please

A. 3.0
B. 1.8
C. 1.0
D. 2.5

Help me pleaseA. 3.0B. 1.8C. 1.0D. 2.5

Answers

Answer:

The average GPA would be 1.8

Step-by-step explanation:

Hope this is helpful. I did a test like this exact question and I got it right.

what is 5r^(2)-14r+ 8 =
in general trinomial

Answers

Answer:

STEP

1

:

Equation at the end of step 1

(5r2 - 14r) + 8

Step-2 : Find two factors of 40 whose sum equals the coefficient of the middle term, which is -14 .

-40 + -1 = -41

-20 + -2 = -22

-10 + -4 = -14 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -4

5r2 - 10r - 4r - 8

Step-4 : Add up the first 2 terms, pulling out like factors :

5r • (r-2)

Add up the last 2 terms, pulling out common factors :

4 • (r-2)

Step-5 : Add up the four terms of step 4 :

(5r-4) • (r-2)

Which is the desired factorization

Final result :

(r - 2) • (5r -4)

5r^2-14r+8 is the awnser

factor the trinomial. use the steps and factor chart for help. x2 5x 6x2 5x 6 remember the format: ax2 bx c

Answers

After factorizing the trinomial x^2 - 5x + 6  the factors are ( x - 3 ) ( x - 2).

Given:

Quadratic equation:

x^2 - 5x +6

= x^2 - 3x - 2x +6

Taking x as common

= x ( x - 3 ) - 2x + 6

Taking -2 as common

= x ( x - 3 ) - 2 ( x - 3 )

Taking (x-3) as common

= ( x - 3 ) ( x - 2 )

Therefore after factorizing the trinomial x^2 - 5x + 6  the factors are

( x - 3 ) ( x - 2).

Learn more about the factor here:

https://brainly.com/question/26923098

#SPJ4

Which is an example of area? the amount of wallpaper for a wall in a bedroom the number of towels I can fit in a bathroom cabinet the amount of ribbon used to decorate from one end of a room to the another

Answers

The example of area is the amount of wallpaper for a wall in a bedroom.

Area is a measure of the two-dimensional space inside a closed shape, such as a rectangle, triangle, or circle. It is typically expressed in square units, such as square meters, square inches, or square feet. In this case, the amount of wallpaper needed to cover a wall in a bedroom is an example of area because it requires measuring the two-dimensional space of the wall in order to determine the amount of wallpaper needed. The wall can be measured by finding the length and width and multiplying the two measurements together to get the total area. The amount of wallpaper needed is then determined by dividing the total area of the wall by the area of a single roll of wallpaper.

The number of towels that can fit in a bathroom cabinet and the amount of ribbon used to decorate a room from one end to another are not examples of area. The number of towels that can fit in a cabinet is a measure of volume, while the amount of ribbon used to decorate a room is a measure of length.

Learn more about Two-Dimensions here: brainly.com/question/17121977

#SPJ11

are people born in certain seasons more likely to be allergic to dust mites? research suggests this might be true. the table below gives the birth seasons of 500 randomly selected people who are allergic to dust mites, along with the proportion of births in the general population for each season. do these data provide convincing evidence that the distribution of birth season is different for people who suffer from this allergy?

Answers

Answer:

Step-by-step explanation:

yes but that is just me go to my page for why i think that

Arthur sits in the park reading a newspaper, then starts walking home at a constant pace. He stops for bagels, then walks the rest of the way home.

Use the graph to answer questions about this scenario.
1. What does the x-axis represent in this situation?


2. What does the y-axis represent?


3. During which parts of the graph does Arthur's distance from home decrease?

4. When is Arthur waiting for bagels? Explain how you know.


5. If Arthur's pace had not been constant after leaving the bagel shop, which part of the graph would change? Explain how that part of the graph would change.



6. If Arthur had spent less time reading his newspaper, which part of the graph would change? How would that part change?

Answers

The answers to each part is below..

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is a graph as shown in the image.

The {x} - axis represents the time.The {y} - axis represents the distance from the home.During the 2nd and 4th part.During the 2nd part, he is waiting for bagels.The 2nd part of the graph would change.The first part would have changed.

Therefore, the answers to each part is given above.

To solve more questions on algebraic equations, visit the link below-

brainly.com/question/1041084

#SPJ1

Arthur sits in the park reading a newspaper, then starts walking home at a constant pace. He stops for
Other Questions
Jack is planning to retire He is going to invest a large sum of money right now that he con 51500 wery year ears Ater 25 years with Interest on his investment accounts 7 14% compounded daily. How much Interest will be red stolte 3 years for you and they will much money Jack is investing right now helpppp pls !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I fear that I shall fall.what is the noun clause can someone help pls subtrahend is to subtract; division is to a nurse is teaching the parents of a child with sickle cell disease about factors that predispose the child to a sickle cell crisis. the nurse determines that the teaching was successful when the parents identify what as a factor? 12.345 6 7Theof an interval or chord determines its sound characteristics.O rhythmO notationo qualityO consonance which type of stretch works through myofascial release to reduce soreness and decrease inflammation? quizley River crossed by Akbar was _____ A manufacturer wants to keep track of the average of the ratings that have been submitted for an item using arunning average. The algorithm for calculating a running average differs from the standard algorithm forcalculating an average, as described in part (a).A partial declaration of the RunningAverage class is shown below. You will write two methods of theRunningAverage class.public class RunningAverage{/** The number of ratings included in the running average. */private int count;/** The average of the ratings that have been entered. */private double average;// There are no other instance variables./** Creates a RunningAverage object.* Postcondition: count is initialized to 0 and average is* initialized to 0.0.*/public RunningAverage(){ /* implementation not shown */ }/** Updates the running average to reflect the entry of a new* rating, as described in part (a).*/public void updateAverage(double newVal){ /* to be implemented in part (a) */ }/** Processes num new ratings by considering them for inclusion* in the running average and updating the running average as* necessary. Returns an integer that represents the number of* invalid ratings, as described in part (b).* Precondition: num > 0*/public int processNewRatings(int num){ /* to be implemented in part (b) */ }/** Returns a single numeric rating. */public double getNewRating(){ /* implementation not shown */ }}Write the method updateAverage, which updates the RunningAverage object to include a new rating. To update a running average, add the new rating to a calculated total, which is the number of ratings times the current running average. Divide the new total by the incremented count to obtain the new running average. Select the correct answer. Which compound is inorganic? A soccer player scores 3 goals in 2 games. How many goals are they expected to score in 9 games? Answer without units when dr. hewitt pulls the tablecloth, why do the items on the tablecloth do what they do? environmental conditions of the ocean What is the square root of 6 in a fraction form why is language important in the development of a nation?? (7 marks) ......................... Based on the same principles as above, classify the radioactive decays as alpha emission, beta emission, or electron capture.Alpha emission:Beta Emission:Electron Capture:-40K19-218Po84-226Ra88-234Th90 dinah, a therapist, works with her clients to help them change their problematic behavios and irrational thoughts and provide new, more adaptive behaviors and beliefs to replace old, maladaptive ones. dinah uses what type of therapy? Elevator 1 moved up 10 feet from the ground level. its position is labeled as +10. Elevator 2 moved down 5 feet from the ground level. Its position is labeled as _____ How did the Crusades contribute to the end of Europe's medieval period?A. The Crusades made many Europeans question the authority of theProtestant ChurchB. The Crusades increased the power of the Catholic Church, whichweakened the power of individual kings.C. The Crusades reduced Europe's workforce, making it harder forlords to find laborers.D. The Crusades caused nobles to feel a religious obligation to endfeudalism and manorialism,