F16 Study Guide for Exam 1
Linear Algebra, Dave Bayer
1
Our first exam will be held in class on Tuesday, October 11, 2016. Makeup exams will only be given under
exceptional circumstances, and require
GU 4260 Market Design
Spring 17
Assignment ] 2
Question 1 Take any marriage problem in which agents on one side, say, women, have the
same preferences over the men. Is there a unique stable matching?
6
F16 Study Guide for Exam 1
Linear Algebra, Dave Bayer
[7] By least squares, find the equation of the form y = ax + b that best fits the data
x1
x2
x3
x4
0
y1
1
y2
=
2
y3
3
y4
1
1
1
2
[8] Find a
4
F16 Study Guide for Exam 1
Linear Algebra, Dave Bayer
[6] Find the intersection of the following two affine subspaces of R4 .
1
0
1
w
x
1
r
= 1 + 2
1 2 s
1
y
0
1
1
z
2
1
w
3
1
x
= +
8
F16 Study Guide for Exam 1
Linear Algebra, Dave Bayer
[3] Express A as a product of elementary matrices, where
3 5
A =
1 0
[4] Find the matrix A such that
1
0 1
3
0 0
1 1 = 3
3 0
A 1
0 1 1
0 3 0
[5]
3
F16 Study Guide for Exam 1
Linear Algebra, Dave Bayer
(F15 Homework 1) (Solutions)
[1] Solve the following system of equations.
w
1 1 1 3
3
1 1 2 3 x = 4
y
1 1 3 3
5
z
[2] Using matrix multipl
10
F16 Study Guide for Exam 1
Linear Algebra, Dave Bayer
[2] Using matrix multiplication, count the number of paths of length eight from x to z.
x
y
z
[3] Express A as a product of elementary matrices
5
F16 Study Guide for Exam 1
Linear Algebra, Dave Bayer
[5] Find the intersection of the following two affine subspaces of R4 .
1
0
0
2
w
r
x
1
0
s
= 0 + 1
0 1
0
y
1
t
0
0 1
0
z
1
0
w
9
F16 Study Guide for Exam 1
Linear Algebra, Dave Bayer
[3] Express A as a product of elementary matrices, where
0 1 12
A = 1 0 0
0 0 3
[4] Find the matrix A such that
1
0 1
0 0 3
1 1 = 0 0 3
A 1
0 1
7
F16 Study Guide for Exam 1
Linear Algebra, Dave Bayer
[5] Let V be the vector space R3 , equipped with the inner product
d
2 1 0
1 2 1
e
h(a, b, c), (d, e, f)i = a b c
0 1 2
f
Using this inner pr
F16 Study Guide for Exam 1
Linear Algebra, Dave Bayer
2
Homework will count as 10% of your course grade. The homework for Exam 1 is given below. You may turn in
problems in batchs as you complete them