For each of the following functions, determine whether or not the function is a linear transfor- mation. Either prove that it is a linear transformation or give an explicit counter example to show that it is not a linear transformation. (a) T: P1 → P2 where T(ao +a1x) = ao + a1x + x². (b) T : M2.2 –→ R where T = a + d. (c) T : M2,2 → M2,1 where T
For each of the following functions, determine whether or not the function is a linear transfor- mation. Either prove that it is a linear transformation or give an explicit counter example to show that it is not a linear transformation. (a) T: P1 → P2 where T(ao +a1x) = ao + a1x + x². (b) T : M2.2 –→ R where T = a + d. (c) T : M2,2 → M2,1 where 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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Transcribed Image Text:For each of the following functions, determine whether or not the function is a linear transfor-
mation. Either prove that it is a linear transformation or give an explicit counter example to
show that it is not a linear transformation.
(a) T: P1 → P2 where T(ao +a1x) = ao + a1x + x².
(b) T : M2.2 –→ R_where T
= a + d.
(c) T : M2,2 → M2,1 where T
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