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Unformatted text preview: s of vectors are at the origin by default, so please do so here). What are
FS: Part B: IV, V, VI
A of the
the coordinates ppendix B4 four corners of S ?
Stanley 99: Ch. 6
(self-study) Nov 2 Asymptotic methods Asst #2 Due 9
(b). TVI.1 transforms S to a parallelogram P ,Sophie of whose sides are vectors TA (e1 ) and TA (e2 ).
Introduction corners of P
WhatA.3/ C the coordinates of the four to Prob. Mariolys ?
18 IX.1 Limit Laws and Comb Marni (c). Let Q be Random Structures Discretewith two Sophie equal to the vectors (5, 0) and (3, 4) (we asthe parallelogram Limit Laws
and Limit Laws
sume the initial points of vectors are at the origin by default, so please do so here). What are
FS: Part C
instances of Q?
the coordinates resentations)
of the four corners ofdiscrete
Continuous Limit 2z, y +
A2. Let T1 (x, y, z ) = (x − y + z, 2x − y +Laws 2Marni z ). 13 30
(a). Is T1 one-to-one? 14 Dec 10
(b). Is T1 onto? Quasi-Powers and
Gaussian limit laws Presentations Sophie
Asst #3 Due (c). Is T1 invertible? If so, ﬁnd the inverse of T1 , expressed in the same general form (but with
different numbers) as we gave for T1 a bove.
A3. Let T2 (x, y, z ) = (x − y − z, x − z, 2y ).
(a). Is T2 one-to-one?
(b). Is T2 onto?
Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY
Version of: 11-Dec-09 2 (c). Is T invertible? If so, ﬁnd the inverse of T2 , expressed in the same general form (but with
different numbers) as we gave for T2 a bove. 3. Extra-Practice Questions:
Try these questions for some more practice. The more practice you get the better you will
understand the material and the better you will do on quizzes and exams. C EDRIC C HAUVE , FALL 2013 2 f a cu lty of science
d epa r tm...
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