Let T:R" → R™ be a linear transformation and u, v E R", c is a scalar. Which of the following must be true? Choose ALL that apply. |T (u) +T(v) =T (u+v) |Т (0) — 0 OT(-v)=T(v) |T (cu) +cT (v) = cT (u+ v)

Let T:R" → R™ be a linear transformation and u, v E R", c is a scalar. Which of the following must be true? Choose ALL that apply. |T (u) +T(v) =T (u+v) |Т (0) — 0 OT(-v)=T(v) |T (cu) +cT (v) = cT (u+ v)

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

Let T:R" → R™ be a linear transformation and u, v E R", c is a scalar.
Which of the following must be true? Choose ALL that apply.
|T (u) + T(v) — т(и + v)
ПТ (0) — 0
OT(-v) =T (v)
T (cu)+cT (v) = cT (u+v)

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