- #1

fabbi007

- 20

- 0

## Homework Statement

relation from R^2-->R^2 ( R is real line)

(y1) [0 1] (x1)

(y2) =[-1 1] (x2)

is this left invertible?

if so what is the left inverse?

y1,y2 are element in a 2by 1 matrix, same with x1, x2. the elemenst 0,1,-1,1 are in a 2x2 matrix. I did no know how to represent a matrix here.

## Homework Equations

A mapping is left invertible only if it is one-to-one

## The Attempt at a Solution

The above relation is one-to-one because x is getting mapped into y with a 2 dimensional relation into a 2 dimensional space. If we solve this we get y1=x2; y2=-x1+x2. Hence I concluded it is left invertible. Also the mapping is onto, since the Range of the mapping is yielding Y.

I am not sure how I can find the left inverse now. Any ideas