Problem 10. Show that the mapping A: R² x R² → R defined by ((a, b), (c, d)) → ad – be is bilinear. Show that A(v, w) = -A(w, v) for all v, w in R². Show that the corresponding mapping Cx C- C is given by (z, w) – Im(Zw) and show that this is invariant under rot ation about the origin. That is, if v, w are in R² and v' and w' are their images under rotation by some amount 0, then show that A(v, w) = A(v', w'). Why is %3D this extra-easy with complex numbers?
Problem 10. Show that the mapping A: R² x R² → R defined by ((a, b), (c, d)) → ad – be is bilinear. Show that A(v, w) = -A(w, v) for all v, w in R². Show that the corresponding mapping Cx C- C is given by (z, w) – Im(Zw) and show that this is invariant under rot ation about the origin. That is, if v, w are in R² and v' and w' are their images under rotation by some amount 0, then show that A(v, w) = A(v', w'). Why is %3D this extra-easy with complex numbers?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 34EQ
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