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cos(0)x – sin(0)y] sin(0)x + cos(0)Y T z || నా

cos(0)x – sin(0)y] sin(0)x + cos(0)Y T z || నా

Advanced Engineering Mathematics
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
Determine whether the following transformations are linear. If a transformation is linear, provide a proof that it is linear by verifying that (LT1) and (LT2) hold. (See the definition of linear transformation.) If the transformation is not linear, state one of the properties of a linear transformation that does not hold - either (LT1), (LT2), or the 0 test (see Q5 in Linear Transformations for the 0 test) - and give a counter-example showing that the property fails. (a) Let T : R³ → R° be given by cos(0)x – sin(60)y sin(0)x + cos(0)y T where 0 is some fixed real number. (b) Let T : R → R? be given by (E) 2х — у — 42 T 3x + xyz
Transcribed Image Text:Determine whether the following transformations are linear. If a transformation is linear, provide a proof that it is linear by verifying that (LT1) and (LT2) hold. (See the definition of linear transformation.) If the transformation is not linear, state one of the properties of a linear transformation that does not hold - either (LT1), (LT2), or the 0 test (see Q5 in Linear Transformations for the 0 test) - and give a counter-example showing that the property fails. (a) Let T : R³ → R° be given by cos(0)x – sin(60)y sin(0)x + cos(0)y T where 0 is some fixed real number. (b) Let T : R → R? be given by (E) 2х — у — 42 T 3x + xyz
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