MATH 1210 Assignment 1 Winter 2014
Due date: January 31
1. Use mathematical induction on positive integer n to prove each of the following:
(a)
(b)
(c)
1
n(6n2 3n 1), for n 1 ;
2
3 + 7 + 11 + . . . + (8n 1) = 2n(4n + 1), for n 1 ;
12 + 42 + 72 + + (3n 2)2
MATH 1210 (WINTER 2014): SOLUTIONS TO
ASSIGNMENT TWO
Q1. Consider the polynomial
p(x) = x3 + k x + (3 2 i),
where k is an unknown complex number. It is given to you that if p(x) is divided by 2 x (4 i),
then the remainder is 5 + i. Find the value of k .
S
MATH 1210 Assignment 3
March 07, 2014
Solutions
Question 1. Consider the two points P (1, 2, 3) and Q(2, 3, 1) , and let v = OQ be the
vector with its tail at the origin and with its head at Q .
(a) Find an equation of the line passing through P and Q .
S
MATH 1210 Assignment 3
March 07, 2014
Due: March 14, 2014, in class
Question 1. Consider the two points P (1, 2, 3) and Q(2, 3, 1) , and let v = OQ be the
vector with its tail at the origin and with its head at Q .
(a) Find an equation of the line passing
MATH 1210 (WINTER 2014)
ASSIGNMENT TWO
Due Date: February 14, 2014
Please write clearly. Your submission must be accompanied by the Honesty Declaration to be
found on the course web-page.
Q1. Consider the polynomial
p(x) = x3 + k x + (3 2 i),
where k is a
MATH 1210 Assignment 4
March 21, 2014
Due: March 28, 2014, in class
Question 1.
Consider the following system of linear
w x + 2y 3z
3w 3x + 8y 5z
2w 2x + 5y 4z
3w 3x + 7y 7z
equations:
=
=
=
=
0
0
0
0
(a) Find the reduced row-echelon form of the augment
MATH 2300 Assignment 1 Winter 2014
Due date: January 28
Attempt all questions and show all your work. Attach to Honesty Declaration Form.
1. Rather than use of standard denitions of addition and scalar multiplication in R2 , suppose that these
two operati
Term Test 1
PAGE: 1 of 5
TIME: 50 minutes
EXAMINER: G.I. Moghaddam
DATE: October 9, 2009
COURSE: MATH 2300
NAME:
STUDENT # :
Q1
Q2
Q3
Q4
Q5
Q6
Total (out of 50)
[6] 1. Let u , v and w be vectors in R ; rst dene the Euclidean distance (u, v) and
then prove
Term Test 2
PAGE: 1 of ?
TIME: 50 minutes
EXAMINER: G.I. Moghaddam
DATE: November 9, 2009
COURSE: MATH 2300
NAME:
STUDENT # :
Q1
Q2
Q3
Q4
Q5
Total (out of 40)
[5] 1. Let A, B and C be matrices of size 3 6, 4 3 and 4 4 respectively. Complete
each of the fo
MATH 1210 Assignment 4
March 21, 2014
Due: March 28, 2014, in class
Question 1.
Consider the following system of linear
w x + 2y 3z
3w 3x + 8y 5z
2w 2x + 5y 4z
3w 3x + 7y 7z
equations:
=
=
=
=
0
0
0
0
(a) Find the reduced row-echelon form of the augment
MATH 1210 Assignment 1 Winter 2014
Due date: January 31
1. Use mathematical induction on positive integer n to prove each of the following:
(b)
1
n(6n2 3n 1), for n 1 ;
2
3 + 7 + 11 + . . . + (8n 1) = 2n(4n + 1), for n 1 ;
(c)
24n 32n is divisible by 7 fo