Math 333 (2015) - Homework 1
Due: September 10, 2015.
NAME:
Most of the homework is a selection of exercises chosen from the textbook.
Show your work in each problem.
Staple this sheet to the front of your assignment
1) Section 1.1:
#12
2) Section 1.2:
#5
3) Section 1.3:
#1
4) Section 1.4:
#10
5) Section 1.4:
#20
6) Section 1.4:
#39
7) Section 1.4:
#45
8) Section 1.4:
#46
(Use the IRm×n notation)
9) Let A ∈ IR3×3 be given by


1 2 3

A=
 1 4 1 
2 1 8
Using standard Gaussian elimination A ∼ B where B is upper triangular with ones on the
diagonal:


1 ∗ ∗

B=
 0 1 ∗ 
0 0 1
Here I do not mean reduced echelon form but rather echelon form with ones on the diagonal.
Find elementary matrices Ei such that
E3 E2 E1 A = B
as demonstrated in class. E3 should be a diagonal scaling matrix.