HW8 - ii Show that the image of f i.e f R 2 = f ~v ~v ∈ R...

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MATH 186 – WINTER 2009 HOMEWORK SET 8 Due Friday 03/27 Be kind to your grader, please staple your work! What you need to know: - Taylor polynomials - Linear subspaces; kernel of a linear transformation. What you shouldn’t forget: - Techniques of integrations: by parts, substitution, and partial fractions - Improper integrals - Vector spaces. Ex 1. Let f : R 2 R 3 be the map defined by f ([ x y ]) = h x y x + y i . i) Show that f is injective, but not surjective;
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Unformatted text preview: ii) Show that the image of f , i.e., f ( R 2 ) = { f ( ~v ): ~v ∈ R 2 } , is a linear subspace of R 3 ; iii) Find two vectors ~v, ~w ∈ f ( R 2 ) such that f ( R 2 ) = { α~v + β ~w : α,β ∈ R } ; iv) Find A,B,C ∈ R such that f ( R 2 ) = { Ax + By + Cz = 0 } . From Spivak: Chapter 20: Ex # 7(ii), 7(iv), 10(d), 11(d), 23. Please recycle!...
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