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Let (..) be the usual inner product on the complex vector space (₂[x]. Recall that is a 1-dimensional vector Space over C. Consider the function To C₂[x] → C given by T(g(x)) = (g(x), x) A) Prove that T is a linear transformation. B) Find a basis for the kernel of T.

Let (..) be the usual inner product on the complex vector space (₂[x]. Recall that is a 1-dimensional vector Space over C. Consider the function To C₂[x] → C given by T(g(x)) = (g(x), x) A) Prove that T is a linear transformation. B) Find a basis for the kernel of T.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.2: The Kernewl And Range Of A Linear Transformation
Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...
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Zet <- be the usual inner product on ₂.) the complex vector space (₂[x]. Recall that C is a 1-dimensional vector space over C. Consider the function To C₂ [x] → C given by T(g(x)) =<g(x), x> A) Prove that T is a linear transformation. B) Find a basis for the kernel of T.
Transcribed Image Text:Zet <- be the usual inner product on ₂.) the complex vector space (₂[x]. Recall that C is a 1-dimensional vector space over C. Consider the function To C₂ [x] → C given by T(g(x)) =<g(x), x> A) Prove that T is a linear transformation. B) Find a basis for the kernel of T.
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