Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    8
    ReputationRep:
    I am having trouble with this question, could anyone give me any tips?Name:  q48.PNG
Views: 4
Size:  20.8 KB
    Offline

    17
    ReputationRep:
    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.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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