a)Let T: P₂ (R) → M₂x2 (R) be defined by T (p) = [(0)()] Find the matrix associated to 7 withrespect to the standard bases = (1.x.x²) and y ==36 36 36 of P₂ (R) andMzxz (R) respectively.b) Let T: R→ R³ be the linear transformation defined byT(x,y,z,u) = (x + 2y, x-3z +u, 2y + 3z + 4u). Let a and ß be the standard bases for R$ andR³ respectively. Find [7]

Answered: Image /qna-images/answer/26d8d71e-42d7-47fa-afec-7258c33560e3.jpg

Answered: Let T: P₂ (R) → M2x2 (R) be defined by…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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1. Let A = MB (f) be the matrix associated with the linear map f(x,y.z) = (3x-y+4z.y+z-x.x+y+z) relative to the bases B={u=(4,18,6), v= (17.1.0), w=(17,0,-5)} and B'= {u'=(2,2,1); v' = (1,0,0); w'=(3,2,0)) Then the first column of A is: OA-16 OB. 4 17 17 B 0 (3) 13 1 OC. 3 O D./ O E. 7-
11. If the matrix of a linear transformation T ::: F. (C) with respect to the ordered basis B = {(1, 0), (0, 1)} is i %3D i) Find the matrix of T with respect to ordered basis B' = {(1, 1), (1, – 1)} %3D
4. Let the linear transformation T: R² → R³ be defined by T(x, y) = (x, 2y, x − y). Find the matrix for Trelative to the bases B = { (4, 2), (3, −1) } and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1) }, and use it to find T(1, 3).
Suppose that T:R²→ R³ is a linear transformation and T(1,-3)=(4,–3, 1) and T(1,4)=(1,3, 1) and let B={(1,–3),(1,4)}. a) Find the matrix representation of Tin terms of B and S3 [T] where S3 is the standard basis for R'. b) Find the change of basis matrix [C, to convert from the standard basis in R? to B. c) Find [T] = [TCE, ->
Suppose T is a linear transformation on R² (i.e. T(x, y) = (ax + by, cx + dy) where a, b, c, d are real numbers and, interpreting T as a matrix, det(T) # 0. Let P be the parallelogram which is the image of the square D = = [0, 1] × [0, 1] (i.e. T(D) =P). Then the area of P is given by O lad - bcl ad bc abcd 1 |ad - bc| O labcd|
1. Let A=MB (f) be the matrix associated with the linear map f(x,y,z) = (3x-y + 4z,y+z-x,x+y+z) relative to the bases B={u=(4, 18,6), v= (17.1.0), w (17,0,-5) } and Then the first B'= {u'=(2,2,1); v' = (1,0,0); w'=(3,2,0) } column of A is: O A. 2 "B 1 3 B. - - 16 On () 13 1 C. D. E. 7 -5 3 4 17 17 3 -
as Find the matrix of the linear transformation T: R →R defined 8. T (x, y, z) = (2x - 3y + 4z, 5x – y + 2z, 4x + 7y) with respect B = {(1,0, 0), (0, 1, 0), (0, 0, 1)} and B' = {(1, 1, 1), (1, 1, 0), (1, 0, 0)}. to the bases %3D %3D %3D
1. Let A = MB (f) be the matrix associated with the linear map f(x,y,z) = (2x − 2y+z, x − 4y+z, x-y-z) relative to the bases B={u=(5,16,1); v= (2, 1, –4); w=(7,17,2)} and B'={u'=(2,0,1); v' = (1,0,1); w'=(3,2,0)) Then the second column of A is: *) 0 O A. (0 O B. "B) °) SOC. O D. (6)
1. Let A = MB (f) be the matrix associated with the linear map f(x,y,z) = (3x−y+4z,y+z−x,x+y+z) relative to the bases B={u=(4,18,6), v= (17.1.0), w=(17,0,−5)} and B'={u'=(2,2,1); v'=(1,0,0); w'=(3,2,0) } Then the first column of A is: OA.-16 O B. 13 1 4 17 17 °C) O D. (2 213 O E. "G) ņ m
Consider the vector space V of all the real polynomials of degree less than or equal to three, p(x) = ax^3 + b x^2 + c x + d, and consider the linear transformation T: V ------> V given by the derivative, i.e., T( p ) = p' = 3ax^2 + 2 b x + c. Find the eigenvalues and eigenvectors of this transformation.

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