1. Let V be the vector space over R, consisting of all complex polynomials of degree at most 2; i.e. V = {ao + a₁ + a₂z² | a₂ € C}. (a) Find a basis for V. Give proper reasons. (b) Find the dimension of V.

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Let V be the vector space over R, consisting of all complex polynomials of degree at
most 2; i.e. V = {ao + a₁x + a₂x² | a₁ € C}.
(a) Find a basis for V. Give proper reasons.
(b) Find the dimension of V.
Transcribed Image Text:1. Let V be the vector space over R, consisting of all complex polynomials of degree at most 2; i.e. V = {ao + a₁x + a₂x² | a₁ € C}. (a) Find a basis for V. Give proper reasons. (b) Find the dimension of V.
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