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).
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).
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 12CM
Related questions
Question
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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53d7cf85-38ef-4e29-990a-1b88e048b96f%2Fca0e6dcb-bbf8-4907-84c7-27bb2ad37f7a%2Fwtqntqt_processed.jpeg&w=3840&q=75)
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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