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
fgiga [73]
3 years ago
9

The following polynomials are the first five in the sequence known as Chebyshev polynomials of the first kindT0(x)=1, T1(x)=x, T

2(x)=2x2 −1 T3(x)=4x3 −3x, T4(x)=8x4 −8x2 +1.(a) Show that {T0, T1, T2, T3, T4} is a basis for P4, the space of polynomials of degree ≤ 4.(b) Check that differentiation defines a linear transformation TD : P4 → P3 and write down the matrix of each linear transformation in the Chebyshev basis. Similarly, check that integration is a linear transformation TS : P3 → P4.(c) Let D and S be the differentiation and integration matrices, respectively, from part (b). Compute the matrix products DS and SD. Interpret the results using calculus: choose a suitable polynomial in P4, differentiate it, and then integrate it.(d) Write down bases for the null spaces and column spaces of D and S. Provide the cor- responding polynomials. Can you interpret your results about D and S in light of what you know about differentiation and integration from calculus?

Mathematics
1 answer:
Artyom0805 [142]3 years ago
4 0

Answer:

Step-by-step explanation: see attachment below

You might be interested in
8. La semana pasada, John gasto $ 18 en 4 juegos de bolos. Esta semana gastó $ 27 en 6 juegos de bolos. John tiene su propio par
irinina [24]

Answer:

Step-by-step explanation:

las quenos juegos = 18

8 0
3 years ago
On average, the merchandise shop sells 80 CDs for every 1 vinyl record. Estimate how many vinyl records they are likely to sell
sp2606 [1]
The merchandise shop sells 80 CDs for every 1 vinyl record. We have to find how many vinyl records they are likely to sell if the merchandise shop sells 760 CDs:
         80  CDs -------------------- 1 vinyl record
        760 CDs --------------------- x vinyl records
     ---------------------------------------------------------
        80  : 760 = 1 : x
        80 x = 760
        x = 760 : 80
        x = 9.5  or 9 ( we need a whole number )
       Answer: They are likely to sell  9 vinyl records.
7 0
4 years ago
Read 2 more answers
1. What is the volume of the following cone? *<br> 2.5 mm<br> 1<br> 12.6 mm<br> 1
mafiozo [28]

Answer: V=πr2h 3

=π·2.52·12.6 3

=82.46681

Step-by-step explanation:

3 0
3 years ago
Micah jogged 8/10 of a mile. Sarah jogged 3 times this distance. How far did Sarah jog?
alexdok [17]

Answer:

8/10 * 3 = (8*3)/10 = 24/10 = 2.4 miles

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
What is the image point of (2, 4) after a translation left 4 units and down 1 unit?
Kitty [74]

Answer:

the answer is (-2,3)

Step-by-step explanation:

when moving to the left you going across the x axis 4 times and going down once om the u axis

8 0
3 years ago
Other questions:
  • Complete the following proof.
    7·2 answers
  • The sum of three consecutive even integers is 288288. find the integers.
    11·1 answer
  • If u dont know dont worry about it
    15·1 answer
  • How do you figure this out?
    12·1 answer
  • 7. Write two trinomials whose difference is 3x - 5x - 6.
    15·1 answer
  • Please help, I need three numbers
    10·2 answers
  • Mhanifa can you please help me on this question? I will mark brainliest!
    7·1 answer
  • Use a model to divide 2÷1/3​
    12·1 answer
  • A polygon with 189 diagonals is called​
    13·2 answers
  • Identify the y-intercept of the graph.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!