Math 1229A/B
Unit 4:
Vectors in m
(text reference: Section 2.1)
c V. Olds 2010
Unit 4
4
51
Vectors in m
Weve learnt about 2 and 3 , which youve seen before. Now, were going to extend some of
the same ideas to spaces with more than 3 dimensions. We refer t
1
Section 2.2 # 23
We need to find the value(s) of c for which the given system has solutions other
than the trivial solution (x, y, z) = (0, 0, 0). (Note that the system always has
this solution, for all values of c.) That is, we need to find the value(s
1
Math 1229A Test 1, October 2016
Answers Code 333
Part A
1.
B
7.
D
13. C
2.
8.
14.
C
A
B
3.
9.
15.
D
A
A
4.
10.
16.
A
B
E
Part B
19. k = 9
20. point of intersection is (x, y) = (9, 4)
21. area =
11
2
5.
11.
17.
E
C
D
6.
12.
18.
B
E
D
1
Math 1229A Test 1, October 2016
Answers Code 111
Part A
1.
D
7.
A
13. D
2.
8.
14.
A
B
A
3.
9.
15.
B
E
E
4.
10.
16.
C
C
D
Part B
19. k = 10
20. point of intersection is (x, y) = (1, 1)
21. area =
17
2
5.
11.
17.
B
D
C
6.
12.
18.
E
A
B
1
Math 1229A Test 1, October 2016
Answers Code 444
Part A
1.
C
7.
C
13. A
2.
8.
14.
E
E
D
3.
9.
15.
A
D
B
4.
10.
16.
B
E
C
5.
11.
17.
Part B
19. k = 11
20. point of intersection is (x, y) = (1, 1)
21. area =
17
2
C
A
D
6.
12.
18.
B
B
E
1
Math 1229A Test 1, October 2016
Answers Code 222
Part A
1.
E
7.
E
13. B
2.
8.
14.
B
D
C
3.
9.
15.
C
B
D
4.
10.
16.
B
A
E
Part B
19. k = 8
20. point of intersection is (x, y) = (7, 2)
21. area =
11
2
5.
11.
17.
A
E
A
6.
12.
18.
C
C
D
Friday, October 14, 2016
Page 1
Mathematics 1229A
Test 1
CODE 222
PART A (18 marks)
1. [ 1
mark ] Which one of the following is not a unit vector?
A: (0, 1, 0, 0, 0)
4
3
C: , 0, , 0
5
5
B: (0, 1)
D:
1
1
,
2
2
1 1 1
3, 3, 3
Solution: A unit vector is a v
Friday, October 14, 2016
Page 1
Mathematics 1229A
Test 1
CODE 111
PART A (18 marks)
1. [ 1
mark ] Which one of the following is not a unit vector?
A: (0, 1)
B:
1
1
,
2
2
4
3
C: , 0, , 0
5
5
D:
1 1 1
, ,
3 3 3
Solution: A unit vector is a vector whose ma
October 2016
Page 1
Mathematics 1229A
Test 1 - Makeup
CODE 444
PART A (18 marks)
1. [ 1
mark ] Which one of the following is not a unit vector?
A:
1
1
,
2
2
4
3
B: , 0, , 0
5
5
C:
1 1 1
, ,
3 3 3
D: (0, 1, 0, 0, 0)
Solution: A unit vector is a vector wh
1
Section 2.3 # 21
We need to solve the given SLE. As always, we form the augmented matrix for
the system and row reduce.
This solution was requested because the solution in the solutions booklet
takes advantage of certain values in the matrix, making uno
1
Section 3.2 # 17
1 2
has
3
c
no inverse. To do this, we try to find the inverse of the matrix, and identify
under what circumstances we would be unable to find an inverse.
We need to find the value(s) of c for which the matrix A =
We start our usual pro
1
Section 2.2 # 24
We need to find the value(s) of k for which the given system has no solution.
We form the augmented matrix for the system
1 1
2
1 1
2 0
0
1 1 k 0
1 1
1
2 3 1
0
1 1
and row reduce. We get:
1 0
1
0
k
k 0 1 1
k
1
0 0
0 1k
Now, we think a
Math 1229A/B
Unit 5:
Systems of Linear Equations
(text reference: Section 2.2)
c V. Olds 2010
61
Unit 5
5
Systems of Linear Equations
You know what the standard form of an equation of a line in 2 looks like. It has the form
ax + by = c, for some constants
Math 1229A/B
Unit 6:
Row Reduction
(text reference: Section 2.3)
c V. Olds 2010
69
Unit 6
6
Row Reduction
Next, we learn a method known as row-reduction for solving SLEs. This method works in basically the same way as the method we used in the previous un
Math 1229A/B
Unit 1:
Vectors
(text reference: Section 1.1)
c V. Olds 2010
Unit 1
1
1
Vectors
You are familiar with the set of real numbers. Real numbers means all the numbers youve
ever heard of or can imagine (unless youve learnt about, or at least heard
Math 1229A/B
Unit 2:
Products of Vectors
(text reference: Section 1.2)
c V. Olds 2010
15
Unit 2
2
Products of Vectors
In Unit 1 we learnt about a variety of arithmetic operations we can do with vectors. But the
only kind of multiplication we learnt about
Math 1229A/B
Unit 3:
Lines and Planes
(text reference: Section 1.3)
c V. Olds 2010
30
3
Unit 3
Lines and Planes
Lines in 2
You are already familiar with equations of lines. In previous courses you will have written
equations of lines in slope-point form,
Math 1229A/B
Unit 1:
Vectors
(text reference: Section 1.1)
c
V.
Olds 2010
Unit 1
1
1
Vectors
You are familiar with the set of real numbers. Real numbers means all the numbers youve
ever heard of or can imagine (unless youve learnt about, or at least heard
Math 1229A/B
Unit 2:
Products of Vectors
(text reference: Section 1.2)
c
V.
Olds 2010
15
Unit 2
2
Products of Vectors
In Unit 1 we learnt about a variety of arithmetic operations we can do with vectors. But the
only kind of multiplication we learnt about
1
Section 3.2 # 23
We want to use the Method of Inverses to solve the system. To use that
approach, we must first find the inverse of the coefficient matrix. We do this in
the usual way. We have
2 3
A=
3 5
and we get:
2
3
3 1
5 0
0
1
R1 21 R1
R2 R2 3R1
R2
October 2016
Page 1
Mathematics 1229A
Test 1 - Makeup
CODE 333
PART A (18 marks)
1. [ 1
mark ] Which one of the following is not a unit vector?
A:
1
1
,
2
2
B:
1 1 1
, ,
3 3 3
C:
4
3
, 0, , 0
5
5
D: (0, 1, 0, 0, 0)
Solution: A unit vector is a vector w