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1. Define g : V → R³, where V = P1 by g(ax + b) = b- a a+b (a) Find the nullspace of g. (b) Find the nullity of g. (c) Find the range space of g. (Write it as a span) (d) What is the rank of g?

1. Define g : V → R³, where V = P1 by g(ax + b) = b- a a+b (a) Find the nullspace of g. (b) Find the nullity of g. (c) Find the range space of g. (Write it as a span) (d) What is the rank of g?

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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1. Define g : V → R³, where V = P1 by g(ax + b) = b- a a+b (a) Find the nullspace of g. (b) Find the nullity of g. (c) Find the range space of g. (Write it as a span) (d) What is the rank of g?
Transcribed Image Text:1. Define g : V → R³, where V = P1 by g(ax + b) = b- a a+b (a) Find the nullspace of g. (b) Find the nullity of g. (c) Find the range space of g. (Write it as a span) (d) What is the rank of g?
(e) Use a nullity argument to determine whether g injective. (f) Use a rank argument to determine whether g surjective. (g) Find a matrix representation of g : V → R³, where V = P1 by g(ar+ b) = b- a a +b (h) Find a basis for the Column Space of this matrix.
Transcribed Image Text:(e) Use a nullity argument to determine whether g injective. (f) Use a rank argument to determine whether g surjective. (g) Find a matrix representation of g : V → R³, where V = P1 by g(ar+ b) = b- a a +b (h) Find a basis for the Column Space of this matrix.
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