The transformation is from the base B to the base C. Problem 5 Let T : P2 → P2 be the linear transformation defined by T(p(x)) = p(x+ 2).Find the matrix representation [T]c,B of T with respect to the ordered basesB = {1,x + 2, (x + 2)?}andC = {1, x, x²}.Check that the representation is correct by computing T(a + bx + cx?) both directly and byusing the matrix representation.

Answered: Image /qna-images/answer/29f90887-42c7-4195-9879-2b17165d14c1.jpg

Problem 5 Let T : P2 → P2 be the linear transformation defined by T(p(x)) = p(x + 2). Find the matrir representation [T]c,g of T with respect to the ordered bases B = {1,x +2, (x +2)²} and C = {1,x, x²}. Check that the representation is correct by computing T(a + bx + cx?) both directly and by using the matrix representation.

Problem 5 Let T : P2 → P2 be the linear transformation defined by T(p(x)) = p(x + 2). Find the matrir representation [T]c,g of T with respect to the ordered bases B = {1,x +2, (x +2)²} and C = {1,x, x²}. Check that the representation is correct by computing T(a + bx + cx?) both directly and by using the matrix representation.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 11CM

See similar textbooks

Related questions

Q: 2. [2x(x²-1) dx 3. 4 √(2x² - 5x+3)( 21² 5x² + 3x) a dx 3 2

Q: Consequently, we get b P+Q= (42) [e (1 – C)– d (A+B+D)]’ where e (1– C)-d (A+B+D) > 0, eb² (1–C) PQ=…

Q: determine

Q: - Multiply by d. b< dXn-1 < XN-1 <1 d or dXN-1 2 b

Q: Theorem 3 Assume that a <1 and 16 (e +g +s) – d (c+f +r)|+|c(d +g +s) – e (b+ f +r)| +|f (d +e +s) –…

A: Given:…

Q: 8.7.1 Example A Consider the following equation (D – a)(A – b)y(æ) = 0, (8.268) where (a, b) are…

A: Given: Consider the following equation ,D-a∆-byx=0

Q: immediately from (13) that the inequality (19) holds. There exist two positive distinctive real…

Q: The main aim of this study is to exhibit some cases on the periodic character of the positive…

A: The equation given to us is as follows:…

Q: The second-order equation Yk+2 Yk+1 – k²yk = 0 (3.159) can be written in the following factored…

A: Given difference equation is yk+2-yk+1-k2yk=0 (i) The factored form…

Q: Theorem 6 If (b+f) > (c+r) and (d+ g) > (e+ s), then the necessary and sufficient condition for…

A: Given : P=aQ+b+fP+c+rQd+gP+e+sQ, Q=aP+b+fQ+c+rPd+gQ+e+sP

Q: Problem 6 Sketch the graphic of the following rational function: f(x) = I - x² 1

A: The domain of the function is a set of all elements where the function exists Range the value of the…

Q: Xn+1 = f (n, Xn-k), n = 0, 1, · · ..

Q: (E – E2 – 1)z(k, l) = 0 (5.51) or (E1 + V1+ E2)(E1 – V1+ E2)z(k, l) = 0. (5.52) We will obtain a…

A: Explanation: Solution of a linear difference equation: First we see how to find the solution to a…

Q: 1 2 2 3 4 5 6 7 8 2 1 6 3 5 7 8 4 2 1

Q: area bounded by f(x) = 9x² – 2x + 1, the x-axis, x = -2 and x = 1

Q: In each item, you are given a set of vectors S the vectors into the columns of a matrix A rref R of…

A: As per our guideline we are supposed to answer first three subparts.kindly repost other question.…

Q: Theorem 6 If (b+ f) > (c+r) and (d + g) > (e + s), then the necessary and sufficient condition for…

A: In the given question we have to determine red, which is let…

Q: The system of difference equations for uz and vk given by (2E – 3)uk + 5vk = 2, 2uk + (E – 2)vk = 7…

A: Given that, (2E-3)uk+5vk=2........(1)2uk+(E-2)vk=7.........(2) Multiply the (2) by 5 and (1) by…

Q: 19. f(x) = (x² – 5)3 -

A: Given: fx=x2-53 to find the where the function is increasing, decreasing, where its concave upward…

Q: Example K Consider the equation Yk+1 (2 cos o)yk + Yk-1 = 0, cos o + 0, (4.82) - where o is a…

A: Given that yk+1-2cos ϕyk+yk-1=0, cos ϕ≠0, where ϕis a constant. To find the solution:

Q: Theorem 10 Every solution of Eq. (8) satisfies both of the following asymptotic relations Yn+1 lim n…

A: We shall clear the doubts in next step. Please follow the given information carefully so that you…

Q: (32-120°)+(14120°) b. (Express your answer in exponential form) (4-i)(-1-1)

Q: (E – E2 – 1)z(k, l) = 0 (E1 + V1+ E2)(E1 – /1+ E2)z(k, l) = 0. %3D

A: The given expression is: E12-E2-1zk,l=0

Q: show me the steps of determine blue

A: We have to check the given solution.

Q: Display addition and multiplication tables for Ζ8.

Q: 4.2.4 Example D The Fibonacci difference equation is Yk+2 = Yk+1+ Yk- (4.40) The Fibonacci sequence…

Q: Example E The third-order equation Yk+3 – Yk+2 – 4yk+1 +4yk = 1+ k+2* (4.235) can be expressed in…

A: We know Eh(yk)=y(k+h)yk+3= E3(yk)yk+2= E2(yk)yk+1=…

Q: p –1 = (r² + 1)(r2 – 1) = (r + i)(r – i)(r + 1)(r – 1), (= %3D

A: Given that, the characteristic equation is r4-1=0. r4-1=0r4=1

Q: = a, duo b (e uz+g uz+s u4) – d (c uz+f u3+r us) (d ui+e uz+g uz+su4)² aF(u0,...,us) %3D Ine…

A: we have introduce a continuous function F:0,∞5→0,∞ which is defined by…

Q: 32° Y

A: solution:-TY¯ and ZW¯ are diameterTU¯ and UX¯ are tangentin right triangle…

Question

The transformation is from the base B to the base C.

Problem 5 Let T : P2 → P2 be the linear transformation defined by T(p(x)) = p(x+ 2).
Find the matrix representation [T]c,B of T with respect to the ordered bases
B = {1,x + 2, (x + 2)?}
and
C = {1, x, x²}.
Check that the representation is correct by computing T(a + bx + cx?) both directly and by
using the matrix representation.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Area$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.
Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find T(7,2).
Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
1. Let Ta : ℝ2 → ℝ2 be the matrix transformation corresponding to . Find , where and .
Find a basis for R3 that includes the vector (1,0,2) and (0,1,1).
Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
Consider the matrices R=[ 0110 ] H=[ 1001 ] V=[ 1001 ] D=[ 0110 ] T=[ 0110 ] in GL(2,), and let G={ I2,R,R2,R3,H,D,V,T }. Given that G is a group of order 8 with respect to multiplication, write out a multiplication table for G. Sec. 3.3,22b,32b Find the center Z(G) for each of the following groups G. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1. Find the centralizer for each element a in each of the following groups. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1 Sec. 4.1,22 22. Find an isomorphism from the octic group D4 in Example 12 of this section to the group G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of Section 3.1. Sec. 4.6,14 14. Let G={ I2,R,R2,R3,H,D,V,T } be the multiplicative group of matrices in Exercise 36 of section 3.1, let G={ 1,1 } under multiplication, and define :GG by ([ abcd ])=adbc. Assume that is an epimorphism, and find the elements of K= ker . Write out the distinct elements of G/K. Let :G/KG be the isomorphism described in the proof of Theorem 4.27, and write out the values of .
Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices (3,5), (5,3) and (3,0) counterclockwise 90 about the origin. Graph the triangles.
a Let T=[3001]. What effect does T have on the gray square in Table 1? b Let S=[1002]. What effect does S have on the gray square in Table 1? c Apply S to the vertices of the square, and then apply T to the result. What is the effect of the combined transformation? d Find the product matrix W=TS. e Apply the transformation W to the square. Compare to you final result in part c. What do you notice?