Turn on thread page Beta
    • Thread Starter

    I am having trouble with this question, could anyone give me any tips?Name:  q48.PNG
Views: 7
Size:  20.8 KB

    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 b_i.

    For uniqueness, just suppose that two maps L_1 and L_2 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 b_i since the b_i form a basis and so span R^p.
Submit reply
Turn on thread page Beta
Updated: November 10, 2017


students online now


Exam discussions

Find your exam discussion here

Should predicted grades be removed from the uni application process
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

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

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

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.