Question: Let T: P2 P2 be a linear transformation for which T(l + x) = 1 + x2, T(x + x2) = x - x2,

Let T: P2 → P2 be a linear transformation for which
T(l + x) = 1 + x2, T(x + x2) = x - x2,
T(1 + x2) = 1 + x + x2
Find T(4 - x + 3x2) and T(a + bx + cx2).

Step by Step Solution

★★★★★

3.46 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We do the second part first then substitute for a b and c to get the first part We must find the c... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

859-L-A-L-S (2761).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let T: R2 P2 be a linear transformation for which Find =1-2x and T x+2x2 0 and T

Let T: R2 R3 be a linear transformation for which Find 304 0 121 7 Tand T

Let T: M22 R be a linear transformation for which Find 2 4 10 11 10 11 00 10 1011 1 2 4 and Ta b

need answer asap, with proper working. 6. (20 points) Let T : P2 - P2 be the linear transformation given by T(f(x)) = 2xf (x) +x'f (x) + 3f(x) Let B = {1, (x+1), (x+1)2} and B = {1, (x - 1), x } be...

1. (2 points) Let T: P2 P3 be the linear transformation defined by 3x T(p(x)) = (x + 1)p(x) + p'(1) + 2p(t) dt. Find [7], the matrix of T relative to the standard bases of P ({1,2,2}) and Ps ({1, x,...

LINEAR ALGEBRA, PLEASE ANSWER THE FOLLOWING QUESTION Question 5 10 pts Let T: P2 - P3 be a linear transformation defined by T(p(x)) = (x+1)p(x-2) and let B = { x2, x, 1 } and C = {x3, x2, x, 1 } be...

Let T' : P2 - R be a linear transformation. For any polynomial p(I) = ax + br + c in P2, define the transformation by T(ax + ba + c) = [atc [b-20] Use the standard basis B - {x2, x, 1} for P2 and...

shown below 5. (10 points) Let P2(R) be the space of polynomials of degree at most 2 with coefficients in R. Consider the following two bases of P2 (R): a = {1, ac, ac2 } B = {1, 1 + x, +x2]. Let T :...

Let T: P2 P2 be the linear transformation defined by T(p(x)) = xp'(x). (a) Which, if any, of the following polynomials are in ker( T)? (i) 1 (ii) x (iii) x2 (b) Which, if any, of the polynomials in...

Question 2 of 3 Let T : P2 - P2 be the linear transformation defined by T(p(x)) - p(5x + 1), that is I ( co + CI + ( 220 ? ) = co + CI ( 5 :0 + 1 ) + c2 ( 5 x + 1 ) ? (a) Find [T], with respect to...

Which of the following accounts would not appear in the post-closing trial balance? Interest Payable; Equipment; Depreciation Expense; Jennifer Shaeffer, Drawing; Unearned Revenue; Accumulated...

27. Let Qd stand for the quantity demanded, Qs stand for the quantity supplied, and P stand for price. If Qd = 20 - 2P and Qs = 5 + 3P, then the equilibrium price is: O$1 $4 $3 O S2 O O

In an experiment conducted by the Mining Engineering Department at Virginia Tech to study a particular filtering system for coal, a coagulant was added to a solution in a tank containing coal and...

What are some rules of conduct to follow during the interview? (38.2)

Find the orthogonal projection of v onto the subspace W spanned by the vectors u i . (You may assume that the vectors u i are orthogonal.) -1 -2 > -3 , , %3D >

Find the orthogonal decomposition of v with respect to W. W = span -2 2 3

Find the orthogonal decomposition of v with respect to W. 2 -1 W = span| .3

Responsibility Centers A responsibility center is any part of an organization that one manager has control over and is responsible for. A = Cost Center B = Investment Center C = Profit Center For...

Please provide details and explanations!! 5. Compound interest In 2017, Leonardo da Vinci's painting Salvator Mundi sold for a record $450.3 million. In Page 41 1958, it sold for $125, equivalent in...

i need a cash budget thank you so much you have no idea how much i need this 1 The December 31, 20XX, balance sheet for the company follows . DYB-ASPORA, Inoorporated Balance Sheet December 31, 20xx...