Math 319 Test 2 Review
1
1. 2.2 Number 6 Let A be a nonsingular matrix. Show that det(A
)=
1
det(A)
2. Complete the denition of the adjoint of a matrix A
3. 2.3 Number 1 For each of the following, compute (i) det(A), (ii)
0
1
0
!
!
1 3 1
1 1
1 2
3 1
B
C
B
Math 319-1 Test 1 Name:
Student Number:
Show your work completely!
cfw_bf Concepts: Row Echelon and Reduced Row Echelon form, singular and non-singular
matrix, inverse of a matrix, identity matrix, elementary matrices.
1. Use back substitution to solve th
Math 319-1 Test 3 Name: Student Number:
(20 pts) 1. Determine whether the following statements are true or false:
T a. Any four vectors in R3 are linearly dependent.
b. The dimension of the vector space REX2 is 2.
c. The dimension of the vector space R2
54%“?
1. Short Answers. Assume that A and B are arbitary square matrices. (10 points)
Math 319-1 Test 2 Name: Student Number:
3. ® or false: In a vector space, there is a zero element and this zero element is unique.
'“’\
b. True or gee} It is always true
Chapter 1
Set Theory
Introduction
What is Probability?
Review of Set
Theory
A set is a collection of things called elements.
A set is denoted in capital letters and dened by simply
listing its elements in curly brackets. Example:
A = cfw_b, c.
Can also be
Chapter 1
Cardinality in Finite sets
Introduction
What is Probability?
Review of Set
Theory
Review
Venn Diagrams
Set Operations
Cardinality
Functions
Cardinality is basically the size of the set.
Random
Experiments and
Probabilities
If set A only has a ni
Math 319 Syllabus, Fall 2014
T TH 1:00-2:15 Hume 113
Instructor:
O ce:
Email:
Dr. Reid
Hume 314
mmreid@gmail.com
be given without the permission of the Department
of Mathematics. Every student must take the nal
exam at the time scheduled.
Attendance Polic
Names:
Math 319 Quiz 8
1. Consider the following vectors in R2
(a) Determine the length of x1 = (8, 6)T
Solution:
p
p
|x1 | = 82 + 62 = 100 = 10
(a)
(b) Determine the length of x2 = (4, 3)T
Solution:
p
p
|x2 | = 42 + ( 3)2 = 25 = 5
(b)
Math 319 Final Review
1. State the Elementary Row Operations
2. Section 1.2 Number 3 The augmented matrices that follow are in reduced row echelon form. Solve
the corresponding linear system.
0
1
0
1
0
1
1 0 0
2
1 4 0 2
1
3 0
2
B
C
B
C
B
C
(a) @ 0 1 0
(c)
Math 319 Test 2
1. Let A be a nonsingular matrix. Show that det(A 1 ) =
1
det(A)
Solution:
det(A) det(A 1 ) =det(AA 1 ) = det(I) = 1 So det(A 1 ) =
1
det(A)
2. Use Cramers rule to solve the following systems.
x1 + 2x2 = 3
3x1
x2 = 1
Solution:
x1 =
3
1
2
1
Name:
Math 319 Test 3
1. Finish the denition. A mapping from a vector space V to a vector space W is a linear
transformation if
Solution: L(v1 ) = L(v1 )
and
L(v1 + v2 ) = L(v1 ) + L(v2 )
for all v1 , v2 2 V and for all scalars and
2. Complete the denitio
Names:
Math 319 Quiz 5
0
1
B 2 1 1 C
B
C
B
C
B
C
1. Let A = B 6 4 5 C Find elementary matrices E1 , E2 , E3 such that E3 E2 E1 A = U
B
C
C
B
@
A
4 1 3
(U is upper triangular)
Solution:
0
B
B
B
B
Let E1 = B
B
B
@
0
1
B 2 1 1 C
B
C
B
C
B
C
B 0 1 2 C
B
C
B
C
Names:
Math 319 Exit Ticket 1
1. Complete the denition. Two systems of equations involving the same variables are said
to be equivalent if
Solution: they have the same solution set.
2. List three operations on the augmented matrix that result in an equiva