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
andrew11 [14]
4 years ago
13

Let Pk denote the vector space of all polynomials with degree less than or equal to k. Define a linear transformation T : P4 ! P

3 by T(f(x)) = f(0)+f '1)(x-1)+f ''(2)(x-2)^2+f'''(3)(x-3)^3. Find the matrix representation for T relative to the standard basis {1; x; x^2; x^3; x^4} of R4 and the reversed standard basis {x^3; x^2; x; 1} of R3.
Mathematics
1 answer:
shusha [124]4 years ago
6 0

Answer:

Step-by-step explanation:

T(1)=1=0*x^3 0*x^2 0*x 1*1 T(x)=x-1=0*x^3 0*x^2 1*x (-1)*1 T(x^2)=2x^2-6x 6=0*x^3 2*x^2 (-6)*x 6 T(x^3)=6x^3-48*x^2 141*x-141 T(x^4)=24*x^3-204*x^2 628*x-604*1 collect the coefficient matrix and take its transpose

0 0 0 6 24

0 0 2 -48 -204

0 1 -6 141 628

1 -1 6 -141 -604

You might be interested in
Find the amount of discount when the original price is $90 and the discount rate is 10%
Licemer1 [7]
Answer: 81. If you subtract 10% from the amount of 90, you get 81.
3 0
3 years ago
3. A Card is drawn from the deck and is not put back
N76 [4]

Answer:

dependent

Step-by-step explanation:

8 0
3 years ago
What additional information is needed to prove triangle LMN is congruent to triangle KMN using the HL theorem?
IgorC [24]
<h2>Answer:</h2>

∠LMN is a right angle

<h2>Step-by-step explanation:</h2>

If we want to prove that two right triangles are congruent by knowing that the corresponding hypotenuses and one leg are congruent, we begin as follows:

  • Since two legs are congruent and we know this by the hash marks, then the triangle ΔLKN is isosceles.
  • By definition LN ≅ NK
  • If ∠LMN is a right angle, then MN is the altitude of triangle ΔLKN
  • Also MN is the bisector of LK, so KM ≅ ML
  • So we have two right triangles ΔLMN and ΔKM having the same lengths of corresponding sides
  • In conclusion, ΔLMN ≅ ΔKMN
3 0
3 years ago
Read 2 more answers
How do you graph inverse functions?
balu736 [363]
A function and its inverse are reflected over the line y = x. To graph a function and its inverse, all you have to do is graph the function and then switch all x and y values in each point to graph the inverse.
3 0
3 years ago
Which equation represents the hyperbola in general form?
valina [46]

ANSWER

D.

9 {y}^{2}  - 4 {x}^{2}- 36y + 16x - 16 = 0

EXPLANATION

The standard equation of the hyperbola is

\frac{ {(y - 2)}^{2} }{4}  -  \frac{ {(x - 2)}^{2} }{9}  = 1

We multiply through by 36 to obtain:

9 {(y - 2)}^{2}  - 4( {x - 2)}^{2}  = 36

We now expand to get,

9( {y}^{2}  - 4y + 4) - 4( {x}^{2}  - 4x + 4) = 36

Expand :

9 {y}^{2}  - 36y + 36  - 4 {x}^{2}  + 16x - 16 = 36

To get the general form, we equate everything to zero to get,

9 {y}^{2}  - 4 {x}^{2}- 36y + 16x - 16 = 0

The correct choice is D.

7 0
3 years ago
Other questions:
  • A plane has an airspeed of 111 km/h. It is flying on a bearing of 79 degrees while there is a 25 km/h wind out of the northeast​
    15·1 answer
  • In AVWX, V X is extended through point X to point Y, mZXVW = (3x + 13)°,
    6·1 answer
  • In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more
    5·1 answer
  • Mr. Hopkins has a 1-meter wire he is using to make clocks. Each fourth meter is marked off and
    6·1 answer
  • PLEASE HELP ME!!!!!!!!!!! NEED ANSWER IN LIKE 6 MINS!!!
    15·1 answer
  • In the number 234.567 in the whole numbers place is _____________?
    11·1 answer
  • A little girl has learned how to write digits. So far, she knows only: one, two,
    10·1 answer
  • ‐(5k – 3) ≤ 15 + 3k :) pls help
    15·2 answers
  • C={X:X is even number X less than n equal to 7}<br>​
    14·1 answer
  • How far can a cyclist travel in 1.5 hours if his average speed is 12 km/hr?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!