# t01 - The University of Sydney Math3061 Geometry and...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The University of Sydney Math3061 Geometry and Topology Web page: www.maths.usyd.edu.au/u/UG/SM/MATH3061/ 2009 Tutorial 1 1. (Revision) ( i ) Given that A = (1 , 1), B = (2 , 3) and C = (4 , 5), find −→ AB , −→ BC and −→ CA . Check your answers by calculating the sum of these three vectors. ( ii ) Find an equation for the line through the point (1 , 1) in the direction given by the vector bracketleftbigg 2 3 bracketrightbigg . 2. Determine (in each case) if the given formula defines α as a transformation of the plane, and if it does, find a formula for the inverse transformation α- 1 . ( i ) α ( x,y ) = ( − y,x + 2), ( ii ) α ( x,y ) = (ln x,y ), ( iii ) α ( x,y ) = ( x − 2 y, − y ), ( iv ) α ( x,y ) = ( x,y + x 2 ). 3. Determine which of the transformations in the previous question are isometries. 4. Given that the transformations α and β are defined by the formulas α ( x,y ) = ( x + y,y ) , β ( x,y ) = ( x − 2 y, − y ) , find formulas for αβ and βα...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

t01 - The University of Sydney Math3061 Geometry and...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online