Turn on thread page Beta
 You are Here: Home >< Maths

# Linear map from basis vectors watch

1. I am having trouble with this question, could anyone give me any tips?
2. The conditions on L already define the whole map implicitly, since linear maps are (uniquely) determined by their action on a basis.
So for existence, just define this map explicitly. That is, define L for any vector in R^p, noting that any such vector can be expressed as a unique linear combination of the basis vectors .

For uniqueness, just suppose that two maps and both satisfy the conditions on L given in the questions and prove that they must be equal at any vector in R^p. Again, remember that any such vector can be expressed as a linear combination of the since the form a basis and so span R^p.

Turn on thread page Beta

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 10, 2017
Today on TSR

### AQA Mechanics Unofficial Markscheme

Find out how you've done here

### 2,987

students online now

Exam discussions

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE