Question: Assume the mapping T: P2 P2 defined by Is linear. Find the matrix representation of T relative to the basis B = [1, t, t2].

Assume the mapping T: P2 †’ P2 defined by
T(a, + aịt + azt?) = 3a0 + (5a, – 2a1)t + (4a1 + a2)t? %3D

Is linear. Find the matrix representation of T relative to the basis B = [1, t, t2].

T(a, + at + azt?) = 3a0 + (5a, 2a1)t + (4a1 + a2)t? %3D

Step by Step Solution

★★★★★

3.40 Rating (181 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Since And since Thus the matrix representation of T relative to the b... View full answer

blur-text-image
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)

Word file Icon

922-L-A-E (339).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

In Exercises 1-3, determine whether the linear transformation T is (a) one-to-one and (b) onto. 1. T: R2 R2 defined by 2. T: R2 P2 defined by = (a-2b) + (3a + b)x + (a + b)X2

Q:

In Exercises 1-3, determine whether the linear transformation T is invertible by considering its matrix with respect to the standard bases. If T is invertible, use Theorem 6.28 and the method of...

Q:

In each case, find the matrix of T: V W If corresponding to the bases B and D of V and IF, respectively. (a)T: M22 R, T(A) = tr A; D = {1} (b) T: M22 M22 , T(A) = AT; (c) T: P2 P3, T|p(x) = xp(x); B...

Q:

Assume the mapping T: P 2 P 2 defined by is linear. Find the matrix representation of T relative to the basis B = {1, t, t}. T (ao + a + at) = 2 ao +(3 a + 4a)t + (5 ao 6a)t

Q:

Assume the mapping T : P2 - P2 defined by Tan + at+ a212) =920 + (4a -6a, ) t+ (2a, + a2) 12 is linear. Find the matrix representation of T relative to the basis B= {1, t, 1 } The matrix for T...

Q:

Please help me find answers to the practice question and please provide work and section number. Exercise 7.5.5: Finding the inverse of a composition of linear functions. Let 71 : R' -> R' and 72 :...

Q:

(1) Prove or disprove : there exist a basis po, pi, p2, pa E PY(R) ( Py(R) is the set of all polynomial over real number with highest possible degree = 3 ) such that none of poly- nomials po. P1, p2,...

Q:

this is the question. 4. (16 points) Recall that P2 is the vector space of polynomials with real coefficients and with degree less than or equal to 2 (equipped with the natural operations on...

Q:

4. Find the determinant of the linear transformation T(f(x)) = f(3x) -6f(x) from P2 to P2. det = 9. Let V = M2x2(R) be the vector space of 2 x 2 matrices and let L : V - V be defined by L(X) = 15 -3...

Q:

1. Consider the transformation T : P2 R3 dened by T (p(t)) = p(0), p(1), p(2) (3x1 matrix) 1a. Show that T is a linear transformation. 1b. Find the matrix for T relative to the bases B and E...

Q:

The following selected items are taken from the accounting records of Amick Corp. at December 31. Sales revenue Cost of goods sold Dividends received on investment in stocks Interest expense Loss on...

Q:

What is a sampling distribution? What do we know about the shape and characteristics of the sampling distribution for M, the sample mean?

Q:

Supermarket chains such as Walmart. Carrefour and Tesco use an extensive range of pricing and non-pricing strategies to compete. Market research published by Which? (a consumer campaigning...

Q:

The following table gives the vapor pressure of water for various temperatures, previously reported in Exercise 5.2. a. Plot a scatter diagram. Does it seem likely that a straight - line model will...

Q:

When a signal is produced from a sequence of measurements made on a process (a chemical reaction, a flow of heat through a tube, a moving robot arm, etc.), the signal usually contains random noise...

Q:

Construct a linear time invariant transformation that has the signal in its kernel. {Xk} = k

Q:

V is a vector space and A is an m n matrix. Justify each answer. (T/F) If B is any echelon form of A, then the pivot columns of B form a basis for the column space of A.

Q:

Troy Engines, Ltd., manufactures a variety of engines for use in heavy equipment. The company has always produced all of the necessary parts for its engines, including all of the carburetors. An...

Q:

prove that the intervals of the form [a,b) are closed in the lower limit topology on R

Q:

nitial Post Instructions After exploring different types of graphs this week, it is unfortunate to learn that there are sometimes misleading graphs used in the news, politics, medicine, etc. in order...