Spring 2014
Math 601
Name:
Quiz 7
Question 1. (4 pts)
Determine whether each of the following statements is true or false. You do NOT need
to explain.
(a) If A is an n n matrix with all entries being integers, then det(A) is also an integer.
Solution: Tru
Spring 2014
Math 601
Name:
Quiz 4
Question 1. (8 pts)
Determine whether the following statements are true or false. If false, explain why.
(a) V is a vector space of dimension n and S is a set of vectors in V . If S spans V ,
then the number of vectors in
Spring 2014
Math 601
Name:
Quiz 3
Question 1. (12 pts)
Determine if the given subset is a subspace of the corresponding vector space. (Show
work!).
(a) (4 pts) The subset of R3 :
W = cfw_v R3 | v (1, 2, 3) = 0
Solution: Yes, W is a subspace. I leave it to
Math 601 Midterm 1
Name:
This exam has 9 questions, for a total of 100 points.
Please answer each question in the space provided. You need to write full solutions.
Answers without justication will not be graded. Cross out anything the grader should
ignore
Spring 2014
Math 601
Name:
Quiz 1
Question 1. (12 pts)
(a) (6 pts) Find equations of the line L that passes through the point A(1, 0, 4, 3) and
is perpendicular to the plane x1 + x2 + x3 + x4 = 1.
Solution: The direction of the line is
(1, 1, 1, 1)
the eq
Spring 2014
Math 601
Name:
Quiz 5
Question 1. (10 pts)
Let F : R2 R2 be the linear transformation dened by
F (x, y) = (3x + 4y, 4x + 3y).
Find the matrix representation of F with respect to the basis S = cfw_u1 , u2 = cfw_(1, 2), (2, 1).
Solution: with r
Spring 2014
Math 601
Name:
Quiz 6
Question 1. (6 pts)
Determine whether each of the following statements is true or false. You do NOT need
to explain.
(a) If S is an orthogonal set of nonzero vectors, then S is linearly independent.
Solution: True.
(b) Fo
Math 601 Final (sample test)
Name:
This exam has 11 questions, for a total of 150 points.
Please answer each question in the space provided. Please write full solutions, not just
answers. Cross out anything the grader should ignore and circle or box the n
Spring 2014
Math 601
Name:
Quiz 9
Question 1. (10 pts)
Evaluate the integral
C
z 2 + sin z
dz
z 2 7z + 6
(a) when C is the circle |z 6| = 2, that is, the circle centered at 6 with radius 2.
Solution: Notice that
z 2 + sin z
z 2 + sin z
=
z 2 7z + 6
(z 1)(
Spring 2014
Math 601
Name:
Quiz 8
Question 1. (10 pts)
(a) Determine whether the function f (z) = x2 y 2 + 2x + i(2xy + 2y) is analytic on C.
Solution: f (z) = x2 y 2 + 2x + i(2xy + 2y). So the real part is u(x, y) =
x2 y 2 + 2x and the imaginary part is
Spring 2014
Math 601
Name:
Quiz 2
Question 1. (10 pts)
Solve the following linear system
2x + 8y + 4z = 2
2x + 5y + z = 5
4x + 10y z = 1
Solution: Set up the augmented coecient matrix
2 8 4 2
2 5 1 5
4 10 1 1
change it to its echelon form
1 4 2 1
0 1 1 1