b) Let T: R³ → P₂ be a linear transformation defined by T(a, b, c) = (3a + 3b) + (−2a + 2b - 2c)x+ ax². i) Find the kernel of T. ii) Is 1 - 2x + 2x2 in the range of T? Explain your answer. iii) Find the nullity (T) and rank (T).

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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Do 4b) i,ii,iii only

QUESTION 4
a) Given the transformation T: M₂×2 → R defined by
T[(a b)]
= a + 2c - d.
Determine whether T is a linear transformation.
b) Let T: R³ → P₂ be a linear transformation defined by
T(a, b, c) = (3a + 3b) + (−2a + 2b - 2c)x+ ax².
i) Find the kernel of T.
ii) Is 1 - 2x + 2x² in the range of T? Explain your answer.
iii) Find the nullity (T) and rank (T).
Transcribed Image Text:QUESTION 4 a) Given the transformation T: M₂×2 → R defined by T[(a b)] = a + 2c - d. Determine whether T is a linear transformation. b) Let T: R³ → P₂ be a linear transformation defined by T(a, b, c) = (3a + 3b) + (−2a + 2b - 2c)x+ ax². i) Find the kernel of T. ii) Is 1 - 2x + 2x² in the range of T? Explain your answer. iii) Find the nullity (T) and rank (T).
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