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Linear Transformation and Inner Product Problem

  • #1
150
2

Homework Statement


  1. Consider the vector space R2 with the standard inner product given by ⟨(a, b), (c, d)⟩ = ac + bd. (This is just the dot product.)

    PLEASE SEE THE ATTACHED PHOTO FOR DETAIlS


Homework Equations


T(v)=AT*v

The Attempt at a Solution


I was able to prove part a. I let v=(v1,v2) and w=(w1,w2)
apply T(v)=AT*v and do the expansions easily yields the result

But for part b I am clueless. Please suggest an attempt
 

Attachments

Answers and Replies

  • #2
535
72
Hint: the expression 'standard representation of ##T##' means 'representation of ##T## in an orthonormal basis'.
 
  • #3
ehild
Homework Helper
15,477
1,854
You can choose any pair of independent vectors u and v to find the matrix elements of the transformation T. Let be these two vectors the base vectors of R2, (1,0) and (0,1).
 

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