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When is a function L: R"→ R a linear transformation? O The function L is one-to-one and onto. O The function must satisfy L(u+ v) = L(u) + L(v) for all vectors u. v in R". O The function must satisfy L(u + v) = L(u) + L(v) and L(cu) = cL(u) for all vectors u v in R" and scalars c. O No conditions are required: all such functions are linear transformations.

When is a function L: R"→ R a linear transformation? O The function L is one-to-one and onto. O The function must satisfy L(u+ v) = L(u) + L(v) for all vectors u. v in R". O The function must satisfy L(u + v) = L(u) + L(v) and L(cu) = cL(u) for all vectors u v in R" and scalars c. O No conditions are required: all such functions are linear transformations.

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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When is a function L: R" → R a linear transformation? O The function L is one-to-one and onto. O The function must satisfy L(u+ v) = L(u) + L(v) for all vectors u. v in R". O The function must satisfy L(u + v) = L(u) + L(v) and L(cu) = cL(u) for all vectors u v in R" and scalars c. O No conditions are required: all such functions are linear transformations.
Transcribed Image Text:When is a function L: R" → R a linear transformation? O The function L is one-to-one and onto. O The function must satisfy L(u+ v) = L(u) + L(v) for all vectors u. v in R". O The function must satisfy L(u + v) = L(u) + L(v) and L(cu) = cL(u) for all vectors u v in R" and scalars c. O No conditions are required: all such functions are linear transformations.
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