Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta

Finding the change-of-coordinates matrix... watch

    • Thread Starter
    Offline

    0
    ReputationRep:
    In P_2, find the change-of-coordinates matrix from the basis B= {1-3t^2, 2+t-5t^2, 1+2t} to the standard basis. Then write t^2 as a linear combination of the polynomials in B.

    My answer...

    P_{c <-- B} = \begin{bmatrix} 1 & 2 & 1 \\0 & 1 & 2 \\-3 & -5 & 0 \end{bmatrix}.

    So, to write t^2 as a linear combination of the polynomials in B...I simply find [x]_B, right?

    Since (P_{c <-- B}) [x]_B = [x]_C = \begin{bmatrix} 0 \\0 \\1 \end{bmatrix}

    \begin{bmatrix} 1 & 2 & 1 & 0 \\0 & 1 & 2 & 0 \\-3 & -5 & 0 & 1 \end{bmatrix} ...I just solved this augmented matrix


    Is my answer correct?

    Thank you in advance...
    Offline

    0
    ReputationRep:
    This is correct.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: April 5, 2011
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
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

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