MAT2022
Answers to Tutorial 3
Section 1.4
15. (a) If A and B are n by n matrices the entry in row i and column j of the matrix product AB is
ai1b1j + ai2b2j + . + ainbnj. Thus if row i of A is all zero this entry in the product is also zero.
This is true
MAT2022
ANSWERS TO TERM TEST 1 - Test A
October 4, 2000
1. (13 marks)
(a) Convert the polar co-ordinates
into cartesian form (x, y);
(b) Convert the cartesian co-ordinates
into polar form
;
(b) Identify the 2-dimensional curve
Multiply by r to get
or x2 +
MAT2022
FW00
ANSWERS TO TERM TEST 1 - Test B
October 4, 2000
1. (13 marks)
(a) Convert the polar co-ordinates
into cartesian form (x, y);
(b) Convert the cartesian co-ordinates
into polar form
;
(b) Identify the 2-dimensional curve
Multiply by r to get
or
MAT2022 Linear Algebra II
FW00F
Answers to Tutorial 1
1. Find the polar coordinates of the points whose Cartesian coordinates are:
(a)
; (b)
Ans. (a)
; (c) (0, 2); (d) (-3, -6).
; (b)
; (c)
; (d)
where the angle must be chosen in the third
quadrant.
2. Fi
MATH 2022: LINEAR ALGEBRA II
COURSE OUTLINE
WINTER, 2010
1. Basic Information
1.1. Instructor: Elissa Ross
e-mail: elissa@mathstat.yorku.ca
Oce: N601A Ross Building
Oce Hours: Wednesday, 4:30pm 5:30pm, Friday 10:30am - 11:30am, by appointment.
1.2. Course
MAT2022
Linear Algebra II
Answers to Tutorial 4
Section 2.2
2. If a matrix is triangular, its determinant is the product of the diagonal elements. Thus for part (a) the
determinant is -30 and for part (b) it is -2. In part (c) rows 1 and 3 are identical s
Answers to Tutorial 9
Anton and Rorres
Section 7.1
See text for answers to questions 1, 2 and 3. However, note that in part (d) the characteristic polynomial
is s2 + 3 = 0 which has complex roots
with corresponding eigenvectors
Note that
you are expected
Answers to Tutorial 8
Anton and Rorres
Section 5.4
1.(a) Since R2 has dimension 2 a basis will only have 2 vectors.
(b) Since R3 has dimension 3 a basis must have 3 vectors.
(c) Since P2 has dimension 3 a basis must have 3 vectors.
(d) Since M22 has dimen
MAT2022 Lin Algebra II
Answers to Tutorial 6
Section 4.1
Questions 1, 5 - see answers in text
13. part (b) of Thm 4.1.2 - demonstrate (u + v).w = u.w + v.w
u.w = -5; v.w = 5; u.w + v.w = 0
u + v = (6, 0, 0, 6); (u + v).w = 0
part (c) of Thm 4.1.2 - demons
MAT2022 Lin Algebra II
Answers to Tutorial 5
Section 3.1
5. (a) Let the initial point of u be P = (x, y, z). Then PQ = (3-x, -y, -5-z). If this is parallel to v then
Thus one possibility is x = -1, y = 2 and z = -4.
(b) As in part (a) if PQ is parallel to