Consider the following functions. f1(x) = x, f2(x) = x2, f3(x) = 2x − 4x2 g(x) = c1f1(x) + c2f2(x) + c3f3(x) Solve for c1, c2, and c3 so that g(x) = 0 on the interval (−[infinity], [infinity]). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {c1, c2, c3} = $$ Correct: Your answer is correct. Determine whether f1, f2, f3 are linearly independent on the interval (−[infinity], [infinity]).

Answers

Answer 1

9514 1404 393

Answer:

(c1, c2, c3) = (-2t, 4t, t) . . . . for any value of tNOT linearly independent

Step-by-step explanation:

We want ...

  c1·f1(x) +c2·f2(x) +c3·f3(x) = g(x) ≡ 0

Substituting for the fn function values, we have ...

  c1·x +c2·x² +c3·(2x -4x²) ≡ 0

This resolves to two equations:

  x(c1 +2c3) = 0

  x²(c2 -4c3) = 0

These have an infinite set of solutions:

  c1 = -2c3

  c2 = 4c3

Then for any parameter t, including the "trivial" t=0, ...

  (c1, c2, c3) = (-2t, 4t, t)

__

f1, f2, f3 are NOT linearly independent. (If they were, there would be only one solution making g(x) ≡ 0.)


Related Questions

Triangle ABC has vertices A(-3,2) B(0,1) and C(-2,-3).
1. Graph triangle ABC and its reflection across the line x=-2?
2. What are the coordinates of triangle A'B'C' if triangle ABC is reflected across the x-axis?
3. What are the coordinates of triangle A'B'C' if triangle ABC is reflected across the y-axis?
4. What are the coordinates of triangle A'B'C' if triangle ABC is reflected across the line y=x?

Answers

If triangle ABC is reflected across the line x = -2, the new point is A'(-1, 2), B'(2, 1) and C'(-2, -3)

If triangle ABC is reflected across the x axis, the new point is A'(-3, -2), B'(0, -1) and C'(-2, 3)

If triangle ABC is reflected across the y axis, the new point is A'(3, 2), B'(0, 1) and C'(2, -3)

If triangle ABC is reflected across the line y = x, the new point is A'(2, -3), B'(1, 0) and C'(-3, -2)

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Triangle ABC has vertices A(-3,2) B(0,1) and C(-2,-3).

1) If triangle ABC is reflected across the line x = -2, the new point is A'(-1, 2), B'(2, 1) and C'(-2, -3)

2) If triangle ABC is reflected across the x axis, the new point is A'(-3, -2), B'(0, -1) and C'(-2, 3)

3) If triangle ABC is reflected across the y axis, the new point is A'(3, 2), B'(0, 1) and C'(2, -3)

4) If triangle ABC is reflected across the line y = x, the new point is A'(2, -3), B'(1, 0) and C'(-3, -2)

Find out more on transformation at: https://brainly.com/question/1620969

Which number is 10 times the value of the 4 in 283.47 ?

Answers

Answer:

No answer sorry.

Step-by-step explanation:

10 times 4 ten thousands = 40 ten thousands = 4 hundred thousands. Explain how you know this equation is true. 10 × 4 ten thousands = 40 ten thousands = 4 hundred thousands.

Answer:

Value of 4= 0.4

10 x 0.4 = 4

Step-by-step explanation:

Solve.

−0.4x−3.1=5.9

Enter your answer as a decimal or as a mixed number in simplest form in the box.

x =

Answers

The solution to the algebraic equation, −0.4x − 3.1 = 5.9, is: x = -22.5

Given the algebraic equation, −0.4x−3.1 = 5.9, to solve for x, follow the steps below:

−0.4x − 3.1 = 5.9

Add 3.1 to both sides

−0.4x − 3.1 + 3.1 = 5.9 + 3.1

-0.4x = 9

Divide both sides by -0.4

-0.4x/-0.4 = 9/-0.4

x = -22.5

Therefore, the solution to the algebraic equation, −0.4x − 3.1 = 5.9, is: x = -22.5

Learn more here:

https://brainly.com/question/16864747

EMERGENCY!!! WILL GIVE THE BRAINLIEST TO THE FIRST ONE RIGHT + 30 PTS!!!

Use the maps below to answer the following question: First image. A map of North America showing the regions of Native American cultures. Second image. A political map of the United States, with all 50 states labeled. Washington, Oregon, and California are on the west coast. Moving east, from north to south, Montana, Idaho, Wyoming, Nevada, Utah, and Arizona are next seen. Then, North Dakota, South Dakota, Nebraska, Colorado, Kansas, Oklahoma, New Mexico, and Texas are seen, from north to south, in the central US. East of those states, from north to south, Minnesota, Iowa, Missouri, Arkansas, and Louisiana are seen. Wisconsin, Michigan, Illinois, Indiana, and Ohio in the Midwest, and Pennsylvania and New York in the northeast, border the Great Lakes. Kentucky, Tennessee, Mississippi, Alabama, Virginia, North Carolina, South Carolina, Georgia, and Florida are in the southeast, with Florida jutting out as a peninsula. Maryland, West Virginia, Delaware, and New Jersey are between the southeast and northeast states. Connecticut, Rhode Island, Massachusetts, New Hampshire, Vermont, and Maine are in the northeast. Alaska and Hawaii are seen as islands. Public Domain © Andrew c Creative Commons, Attribution-Share Alike 3.0 Unported Compare the maps. Which state listed below was located in the Southwest Native American cultural region? Alabama Illinois Michigan Arizona

Answers

The state that was located in the Southwest Native American cultural region is Arizona.

The state has the highest indigenous population in the USA and is home to the Navajo, Hopi and Apache. Arizona was part of New Mexico until its surrender to the United States in 1848. It was the scene of many wars against the native peoples, especially the Apache, from the 1850s to 1877. It did not become a state until as recently as 1912.

On February 28, 1859, the first Indian reservation, the Gila River Indian Reservation, was established for the Pima and Maricopa Indians in the Arizona Territory. On June 1, 1868, the United States' largest reservation, the Navajo Nation Reservation, was established by a treaty between the United States and the Navajo State.

Learn more in https://brainly.com/question/6326323

Answer:

Arizona

Step-by-step explanation:

got it right on the test :)


The farmer has 1 1/2 acres of

land for planting crops. She
plans to divide the acreage into
2 equal crops of corn and
wheat. How much acreage will
she use for planting each crop?

Answers

Answer:

3/4 acre

Step-by-step explanation:

1 1/1 = 3/2

3/2 ÷ 2 = 3/2 × 1/2 = 3/4

how man1/3 are in 2 2/3

Answers

Answer:

that 8/3

Step-by-step explanation:

thats because it goes too 2 2/3

Jonah found that it took him 10 minutes to do 5 math problems. If he uses this information, what should be his estimation on how long it will take him to do 32 math problems? ​

Answers

We can round 32 down to 30.

10 minutes for 5 math problems is the same as 2 minutes for 1 math problem. Therefore, we can estimate that it will take Jonah approximately 60 minutes to do 32 math problems.

Hope this helps!! :)

A bus travels 324 km in 8 hours. How long will it take to travel 243 km ?​

Answers

Answer:

Six hours

Step-by-step explanation:

Answer:

6 hours

Step-by-step explanation:

Use a ratio and cross multiply to solve for x

324       243

------  =  -------

 8            x

324x = (8)(243)

324x = 1944

x = 6

the population in a town is 10,000. The population is growing at a rate of 0.08. what will the population be in 10 years

Answers

Hope this helps have a nice day!!!!

How many songs can Chet download for $1.00 using Get Tunes? If she downloaded 27 for $13.50

Answers

Answer:

2

Step-by-step explanation:

what is the product of the roots of quadratic equation?​

Answers

Product of the roots = c/a = c

Hope this helped you- have a good day bro cya)

By which rule are these triangles congruent?
AAS
ASA
SAS
SSS

Answers

SSS

Two pairs of sides have already been marked congurent.  The third side is shared by the two triangles, so it must be congruent with itself.

You have three congruent sides: SSS

The graph of y = f (x) is given in the figure. Sketch = 1/2 ( + 2) − 2.

Answers

Answer:

y=1/2+2

Step-by-step explanation:

4.0plsss help, will give brianlist

Answers

Answer:

side HG would be proud of the side EF and parallelogram EFGH

Can you please help me with#11?I'm not sure how to find the answer.​

Answers

Answer:

You need to find the x and y intercepts so...

The x intercept is (18,0) since x=18

The y intercept is (0,12) since y=12

Step-by-step explanation:

Cover the y when you are finding the y intercept

Cover the x when you are finding the x intercept

8x/8

144/8

=18

12y/12

144/112

=12

Whats the answer? ( Branliest )

Answers

Answer:

4

Step-by-step explanation:

4-0.25g +0.5h

We have,

g=10

h=5

Putting the values,

4-0.25g +0.5h= 4-0.25*10+0.5*5 =4 -2.5 +2.5 = 4

Answer:

4

Step-by-step explanation:

[tex]4 - 0.25g + 0.5h \\ 4 - 0.25(10) + 0.5(5) \\ 4 - 2.5 + 2.5 \\ 4 \\ [/tex]

PLEASE HELP ME. HAVE TO BE DONE IN FRACTION
3/4 - 7/9 + 2/3 =

Answers

Answer:

23/36

Step-by-step explanation:

use BODMAS

fist add 3/4+2/3

to get 17/12

then subtract 17/12-7/9

to get 23/36

"The quotient of five less than a number and 6, is -4."

Answers

Answer:

The number is 20

Step-by-step explanation:

x represents the missing number

The equation would be:

[tex]\frac{x-5}{6} =-4[/tex]

Then isolate the variable and solve,

First multiply both sides by 6...

[tex]x-5=-25[/tex]

Add 5 to both sides.

x=20

In what base does 126 + 26b = 410?
The base, b, is ___ (Type a whole number.)

Answers

Answer:

11

Step-by-step explanation:

I subtracted 126 from 410 and got 284 then I divided 16 from 284 and got 11

add 4 1/2 + 1 2/5 pls help me its telling me to add extra words srryt

Answers

Answer:

5 9/10

Step-by-step

Have the fraction with common denominators: 5/10 and 4/10

Does anybody know this???

Answers

Answer:

17

Step-by-step explanation:

Let x be the number of books and y the number of CDs,

[tex]x+y=25\\[/tex]

The prices of the products are multiplied with the quantity bought, therefore:

[tex]1.5x + 5y = 65.50[/tex]

Multiplying the first equation by -5, then multiplying the two equations:

[tex]-3.5x=-59.5\\x=17[/tex]

Suppose z varies directly with x and inversely with the square of y . If z=18 when x=6 and y=5 , what is z when x=11 and y=10?

Answers

Z is equal to 8.25 hope this helps you

Please help Giving 15 points

Answers

Answer:

you said you're giving 15 points but its 8

PLEASE HELP, WILL GIVE BRAINLIEST.

Arjun's goal for this week is to drink no more than 100 grams of sugar from all of his beverages combined. The first table shows Arjun's plan for this week. Try to make a DIFFERENT plan to get close to 100 grams of sugar without going over.​

Answers

Arjun could drink 20 grams per day

Purchased goods on credit from Mimi and Ana, RM300 and RM400 respectively. Btw this is account subject and can I know what is the debit and credit for this questions.

Answers

Purchase a/c Dr. 700
To Mimi’s a/c. 300
To Ana’s a/c. 400

How does the graph of g(x) = −(x − 2)4 compare to the parent function of f(x) = x4?

Group of answer choices

g(x) is shifted 2 units to the right and reflected over the x-axis.

g(x) is shifted 2 units to the left and reflected over the x-axis.

g(x) is shifted 2 units to the right and 1 unit up.

g(x) is shifted 2 units to the right and 1 unit down.

Please HELP me

Answers

Answer:

g(x) is shifted 2 units to the right and reflected over the x-axis.

Step-by-step explanation:

James lives 4 miles from the town library. He lives 256 miles from the post office.

How much closer is James to the post office than to the library?

Enter your answer in the box as a mixed number in the simplest form. (Please Help!)

Answers

Answer:

1 1/6 miles

Step-by-step explanation:

i failed the test sooo haha here you go hopefully you dont fail:)

Using the unitary method we can conclude that James is 64 times closer to the post office than to the library.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that James lives 4 miles from the town library.

James lives 256 miles from the post office.

Therefore, we will divide the 256 by 4 to get the answer;

256/4 = 64

Thus, we can conclude that James is 64 times closer to the post office than to the library.

To learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ5

Can an octagon have angles that measure 110°, 75°, 55°, 130°, 145°, 70°, 125°, and 70°?

Answers

Answer: 2.03

Step-by-step explanation:

What is the rate of change for 1

Answers

Step-by-step explanation:

A rate of change is a rate that describes how one quantity changes in relation to another quantity. The rate of change is 401 or 40 . This means a vehicle is traveling at a rate of 40 miles per hour.

A deck of cards has 52 cards with 4 suits (Hearts, Diamonds, Spades, and Clubs) and 13 cards in each suit (Ace thru 10, Jack, Queen, and King; the last three are considered face cards). A card is drawn at random from a standard 52-card deck. What is the probability that the card is not an Ace

Answers

Answer:

12/13

Step-by-step explanation:

P(card is not an Ace) =

(# of ways to not pick an ace) / (# of ways to pick a card from the deck) =

(52 - 4)/(52) =

48/52 =

12/13

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