Math 601 Midterm 2 Sample
This exam has 10 questions, for a total of 100 points + 5 bonus points.
Please answer each question in the space provided. You need to write full solutions.
Answers without j
Spring 2014
Math 601
Name:
Quiz 4 sample
Question 1. (10 pts)
Determine whether the following statements are true or false. If false, explain why.
(a) If a vector space V has dimension n, then any n +
Spring 2014
Math 601
Name:
Quiz 3 sample
Question 1. (10 pts)
Determine if the given subset is a subspace of the corresponding vector space. (Show
work!).
(a) (5 pts) The subset of R3 :
W = cfw_(x, y,
Spring 2014
Math 601
Name:
Quiz 1 sample
Question 1. (12 pts)
(a) (5 pts) Find equations of the line L that passes through the points A(1, 0, 4, 3) and
B(3, 2, 0, 1).
Solution: First, calculate the di
Math 601 Midterm 1 Sample
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 w
Spring 2014
Math 601
Name:
Quiz 5 Sample
Question 1. (10 pts)
Let F : R2 R2 be the linear transformation dened by F (x, y) = (2x+3y, 4x5y). Find
the matrix representation of F with respect to the basi
Spring 2014
Math 601
Name:
Quiz 9 sample
Question 1. (10 pts)
Evaluate the integral
C
ez
dz
z 2 4z + 3
(a) when C is the circle |z 3| = 1, that is, the circle centered at 3 with radius 1.
Solution: No
Spring 2014
Math 601
Name:
Quiz 8 sample
Question 1. (10 pts)
(a) Determine whether the function f (z) = |z|2 is analytic on C.
Solution: f (z) = x2 +y 2 . So the real part is u(x, y) = x2 +y 2 and th
Spring 2014
Math 601
Name:
Quiz 6 Sample
Question 1. (5 pts)
Verify that the rotation matrix A =
cos sin
is an orthogonal matrix.
sin cos
Solution: By denition, we only need to check that
AAT = AT A