Pakistan Degree College of Commerce for Boys, Allama Iqbal Town, Lahore
Array
ECON 200

Fall 2016
Homework 4
due Oct 20, 10pm
1. Let A be an n n matrix such that all its columns are proportional. We can write
A = a1 v a2 v an v
for some column vector v and some scalars a1 , ., an .
a) Find a row vector w such that A = v w.
v1
v2
b) What is the spa
Pakistan Degree College of Commerce for Boys, Allama Iqbal Town, Lahore
Array
ECON 200

Fall 2016
Homework 3
due Oct 13
1. Consider the equations
2x + y = 2
3x + 2y = 2 .
a) Write this system of equations in the form A x = b.
b) Recall the row picture of the equations: each equation cuts out a line in R2 . Is the
intersection of the lines a point, a l
Pakistan Degree College of Commerce for Boys, Allama Iqbal Town, Lahore
Array
ECON 200

Fall 2016
Homework 1
due Sept 29
1. Describe geometrically (line, plane, threedimensional space) the span of
1
2
1
1
1
0
1
1
0
a) 2 and 4
b) 1 and 1
c) 1 and
and
3
6
0
0
0
1
1
1
0
1
d) 1 and 1 and 0
0
1
1
Recall: The span of vectors v and w is
Pakistan Degree College of Commerce for Boys, Allama Iqbal Town, Lahore
Array
ECON 200

Fall 2016
Homework 5
due Oct 27, 10pm
1 2 0 1
1 2 1 0
1. Find LPU and PLU decompositions of A =
0 1 3 1 . Check your answers: once
0 2 2 1
you have a decomposition, multiply out the matrices to make sure you recover A.
2. Suppose u, v, w are column vectors in R3