2.10. Consider the vector field X(x1, x2) = (x1, x2, 1, 0) on R. For teR and pe R?, let o.(p) = a,(t) where a, is the maximal integral curve of X through p. (a) Show that, for each t, q, is a one to one transformation from R2 onto itself. Geometrically, what does this transformation do? (b) Show that Po = identity Pti +t2 = Pt, ° P12 for all t1, t2 e R P-: = 9, 1 for all t e R.
2.10. Consider the vector field X(x1, x2) = (x1, x2, 1, 0) on R. For teR and pe R?, let o.(p) = a,(t) where a, is the maximal integral curve of X through p. (a) Show that, for each t, q, is a one to one transformation from R2 onto itself. Geometrically, what does this transformation do? (b) Show that Po = identity Pti +t2 = Pt, ° P12 for all t1, t2 e R P-: = 9, 1 for all t e R.
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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