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

    what does the det of a 2x2 matrix represent?

    theres a question :

    matrix A :

    1 -2
    2 1

    give a full geometrical description of T

    det of T is obviously 5.
    then all 4 numbers divide by root 5 to find a rotation matrix

    the answer said the enlargement sf is root 5.

    1.does this rule apply to all 2x2 matrix (root of det = enlargement sf)???
    2.is it area enlargement sf or just normal enlargement sf?

    thx a lot
    • Wiki Support Team

    Wiki Support Team
    The matrix A is \sqrt{5} \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix} for some theta, i.e. a rotation followed by an enlargement by a length scale factor of sqrt(5). This certainly doesn't apply to all matrices (most matrices will scale in different directions differently, and they won't be obvious directions), but something similar does. Take the unit square (i.e. the one with corners at (0,0), (0,1), (1,0), (1,1)), and apply the matrix M to it; then the resulting area will be (det M).
Have you ever experienced racism/sexism at uni?
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.