1. Math
  2. Advanced Math
  3. linear algebra isomorphism...

Question: linear algebra isomorphism...

Question details

Linear Algebra: Isomorphism3 n this problem, we consider two 2-dimensional subspaces V, W in R3 and show that they are isomorphic. However there is no canonical isomorphism. We will see this by giving two different isomorphisms from V to W. We define 1 ER 2C3 (i) Define the orthogonal projection f v 3 T3 E 1 E W. This is in fact an isomorphism. T1 from v to W. Give explicitly the inverse map f w V of f, 1.e. write f-1( i explicitly (ii) Give another isomorphism g V W such that g -1 0) and g (4)) What is g 22 for 22 EV? (iii) Show that g is in fact bij ective by showing that Ker(g) 0 and Im(g) W.

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution