mat prob set 1

# mat prob set 1 - University of Toronto DEPARTMENT OF...

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University of Toronto DEPARTMENT OF MATHEMATICS MAT 237y1y Assignment #1 Due date: October 01, 6:10p.m Last Name: _____________________________ First Name ____________________ Student # _______________________________ Lecture Section ______________ (a) TOTAL MARKS: 50 (b) WRITE SOLUTIONS ON THE SPACE PROVIDED, USE THE REVERSE SIDE OF A PAGE TO CONTINUE IF NECESSARY. (c) DO NOT REMOVE ANY PAGES. THERE ARE 6 PAGES (d) FOR A FULL MARK YOU MUST PRESENT YOUR SOLUTION CLEARLY MARKER'S REPORT Question Mark 1 /10 2 /10 3 /10 4 /10 5 /10 TOTAL /50 1

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1. (a) Let a , b , c be any vectors in 3 R . Show that (i) ) ( ) ( c b a c b a × = × (ii) If b a b a = + then a and b are orthogonal. (b) Find the distance between the parallel planes : 1 Π 5 2 2 = + z y x and Π . : 2 20 2 2 = + z y x 2
2. (a) Using the definition of an open set, prove that the subset ) , ( ) , ( 2 2 1 1 b a b a S × = of the Euclidean space 2 R is open. (b) Determine whether the set

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## This note was uploaded on 12/21/2010 for the course MATH 237Y1 taught by Professor Stanczak during the Spring '09 term at University of Toronto- Toronto.

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mat prob set 1 - University of Toronto DEPARTMENT OF...

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