G) = [2х — у] [x + 3y] 1. Determine whether the function T: R? →R? by T is a linear transformation.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I dont know how to answer this question, it would be very helpful, if you could ans this question with a clear explanation for my understanding.

[2x – y]
Determine whether the function T: R² →R? by T (
7(6) =
1.
is a linear
[x + 3y]
transformation.
E)-
[x + y – z]
2ху
2.
Determine whether the function T: R3 →R³ by T
is a linear
=
Lx + z+ 1]
transformation between vector space.
x – 2y
Define a linear operator T: R? →R? by T (E) = |_3,
Determine whether the
4.
|-2x + 4y.
vector v =
is in N(T).
Transcribed Image Text:[2x – y] Determine whether the function T: R² →R? by T ( 7(6) = 1. is a linear [x + 3y] transformation. E)- [x + y – z] 2ху 2. Determine whether the function T: R3 →R³ by T is a linear = Lx + z+ 1] transformation between vector space. x – 2y Define a linear operator T: R? →R? by T (E) = |_3, Determine whether the 4. |-2x + 4y. vector v = is in N(T).
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