(d) V = P₂ (R), W = R³, T(p) = (1,p(1), p(2)), p = P₂ (R); (e) V = P₂ (R), W = R, T(p) = (p(1), p(2), p(3),...), p = P2 (R); (f) V = {x € R: En converges as noo}, W = R, T(x) = limn→ In, x € V;
(d) V = P₂ (R), W = R³, T(p) = (1,p(1), p(2)), p = P₂ (R); (e) V = P₂ (R), W = R, T(p) = (p(1), p(2), p(3),...), p = P2 (R); (f) V = {x € R: En converges as noo}, W = R, T(x) = limn→ In, x € V;
ChapterP: Prerequisites
SectionP.6: The Rectangular Coordinate System And Graphs
Problem 56E
Related questions
Question
part D E F
Transcribed Image Text:In case that both V and W are finite-dimensional and T is a linear mapping, find the
matrix representation M(T) of the mapping assuming canonical basis of V and W.¹ Re-
member that the k-th column of this matrix represents T(uk), where u is the k-th element
of the basis of V. Make sure that if dim(V) = n and dim(W) = m, then you should obtain
m-by-n matrix.
Transcribed Image Text:3 Linear Mappings
In which of the following cases is the mapping TV → W linear (F= R)?
(a) * V = W = R², T(x, y) = (y,x), x, y ≤ R;
(b) V = W = R³, T(x, y, z) = (y-2,2-x, x-y), x, y, z € R;
(c) * V = P₂ (R), W = R², T(p) = (p(1), p(2)), p = P₂(R);
(d) V = P₂ (R), W = R³, T(p) = (1,p(1), p(2)), p = P₂ (R);
(e) V = P₂ (R), W = R, T(p) = (p(1), p(2), p(3),...), p = P₂ (R);
(f) V = {x € R: In converges as n →∞}, W = R, T(x) = limnon, TV;
(g) V =R%, W = R, T(x) = 1 In, I € V;
n=1
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning