c) Let T: Rn → Rm be a linear transformation given by T(x) = A(x). 3 2 0 619) ). 0 0 0 A = 0 1 i) Determine whether T is one-to-one. Give reason(s) for your answer. ii) Determine whether T is onto. Give reason(s) for your answer. iii) Determine whether T-1 exist or not. Give reason(s) for your answer.
c) Let T: Rn → Rm be a linear transformation given by T(x) = A(x). 3 2 0 619) ). 0 0 0 A = 0 1 i) Determine whether T is one-to-one. Give reason(s) for your answer. ii) Determine whether T is onto. Give reason(s) for your answer. iii) Determine whether T-1 exist or not. Give reason(s) for your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Do 4c) i,ii,iii only
![QUESTION 4
a) Given the transformation T: M₂x2 R defined by
T[(b)]= = a +2cd.
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).
c) Let T: Rn → Rm be a linear transformation given by T(x) = A(x).
3 2 0
-619)
0
0
0
0
0.
A =
i) Determine whether T is one-to-one. Give reason(s) for your answer.
ii) Determine whether T is onto. Give reason(s) for your answer.
iii) Determine whether T-1 exist or not. Give reason(s) for your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53d7cf85-38ef-4e29-990a-1b88e048b96f%2F66447d36-2f75-442a-ba90-96b50d0ccd99%2Fuwf901k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QUESTION 4
a) Given the transformation T: M₂x2 R defined by
T[(b)]= = a +2cd.
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).
c) Let T: Rn → Rm be a linear transformation given by T(x) = A(x).
3 2 0
-619)
0
0
0
0
0.
A =
i) Determine whether T is one-to-one. Give reason(s) for your answer.
ii) Determine whether T is onto. Give reason(s) for your answer.
iii) Determine whether T-1 exist or not. Give reason(s) for your answer.
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