Let T : R5 → R³ be given byT(r, y, z, w, t) = (x +y+2z + w – 2t, 2x + y + 4z + w + 5t, 3x + 2y + 6z + 2w + 3t).(a) Find a basis for N(T).(b) Find dim R(T).(C) Is T surjective?(d) Let B = {e1, e2, e3, €4, e5} be the standard basis for Rº. Find a subset of T(B) which is a basis for R(T).

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Let T : R5 → R be given by T(x, y, z, w, t) = (x + y + 2z + w – 2t, 2x + y + 4z + w+ 5t, 3x + 2y + 6z + 2w + 3t). (a) Find a basis for N(T). (b) Find dim R(T). (C) Is T surjective? (d) Let 6 be the standard basis for R5 Find a subset of T(A) which is a basis for R(T)

Let T : R5 → R be given by T(x, y, z, w, t) = (x + y + 2z + w – 2t, 2x + y + 4z + w+ 5t, 3x + 2y + 6z + 2w + 3t). (a) Find a basis for N(T). (b) Find dim R(T). (C) Is T surjective? (d) Let 6 be the standard basis for R5 Find a subset of T(A) which is a basis for R(T)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let T : R5 → R³ be given by
T(r, y, z, w, t) = (x +y+2z + w – 2t, 2x + y + 4z + w + 5t, 3x + 2y + 6z + 2w + 3t).
(a) Find a basis for N(T).
(b) Find dim R(T).
(C) Is T surjective?
(d) Let B = {e1, e2, e3, €4, e5} be the standard basis for Rº. Find a subset of T(B) which is a basis for R(T).

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