(a) Define f : R × R→R×R by f(x,y) = (2x – y, x – 2y). Prove that f is one-to-one. Describe f-1. What is f-1(6, 3)? Show that (fof-1)(x, y) = (f-1 o f)(x, y). {a1, a2, ... , an} where n is a positive integer. Assume that a function (b) Let A = f: A → A is onto. Prove that ƒ is a bijection.

(a) Define f : R × R→R×R by f(x,y) = (2x – y, x – 2y). Prove that f is one-to-one. Describe f-1. What is f-1(6, 3)? Show that (fof-1)(x, y) = (f-1 o f)(x, y). {a1, a2, ... , an} where n is a positive integer. Assume that a function (b) Let A = f: A → A is onto. Prove that ƒ is a bijection.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

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