University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #4
You are expected to work on this assignment prior to your tutorial in the period October 1
October 7, 2015. You may ask questions about thi

MATH 1300 ASSIGNMENT PROBLEMS (UNIT 3)
[10]
1. Determine into which of the following 3 types (A), (B) or (C) the matrices (a) to (e)
below can be classified.
Type (A): The matrix is in both reduced row-echelon form and row-echelon form.
Type (B): The matr

MATH 1300 D01/D02 Winter 2016 Assignment 4
SHOW ALL WORK to get full marks. Leave answers as exact answers. For example,
leave it as fractions such as 1cfw_7 as opposed to decimals such as 0.142857. Word problems
should have sentence answers with units. F

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H
2015/2016
Solutions #4
1. (Fraleigh & Beauregard, pages 226229)
(1) T : F R dened by T (f ) = f (4). For f, g F and R, we have T (f +g) =
(f + g)(4) = f (4) + g(4) =

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H
2015/2016
Solutions #3
1. (Fraleigh & Beauregard, pages 211212)
(2) To nd [x1 , x2 ], the coordinate vector of [2, 4] in R2 relative to the ordered basis,
1
0
2
2
([

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H
2015/2016
Solutions #5
1. (Fraleigh & Beauregard, pages 226229)
(16) Since the j th column of A is T (bj )
B
, A= T
7
4 1 1
1
2
2 2
0
0 =
(18) A v B =
3
0 6

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H
2015/2016
Solutions #2
1. (a) In Z7 , 11 = 1, 21 = 4, 31 = 5, 41 = 2, 51 = 3, 61 = 6.
(b) In Z7 , x2 = 2 if x = 3 or x = 4.
2. (Fraleigh & Beauregard, pages 202203)

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H
2015/2016
Solutions #1
+ 0 1 2
0 1 2
0 0 1 2
0 0 0 0
1. Computing the tables we have
and
. From the tables we
1 1 2 0
1 0 1 2
2 2 0 1
2 0 2 1
see that Z3 is closed

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #3
You are expected to work on this assignment prior to your tutorial in the week of September 24 September 30, 2015. You may ask questions abo

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #5
You are expected to work on this assignment prior to your tutorial in the period October 8
October 21, 2015. You may ask questions about th

Mathematics 206
Solutions for HWK 17a
Section 5.4
Section 5.4 p244 Problem 1. In each part, explain why the given vectors do not form a basis
for the indicated vector space. (Solve the problem by inspection.)
(a) u1 = (1, 2), u2 = (0, 3), u3 = (2, 7) for