Mths 632
May 1, 2008
Not Homework
I not assigning any homework this week, but here are some questions to
m
ponder. I not asking you to write anything. Just ponder.
m
Suppose we have a 3 3 matrix M: It has 9 entries, which we can write as
ai;j ; where the
Maths 632
Solutions to Homework #2
February 14, 2008
Chapter 2.0, Exercises #17, 18, 19
~
#17. We derived a formula that allows us to calculate the projection of any given vector X to the line
~ : The formula tells us that the desired projection is given
Maths 632
Homework #7
April 17, 2008
HW #7: Section 3.4, exercises 2, 4, 6 0 134-135)
(p.
1
0
1
a 0 0
x
2. The transformation given by the matrix @ 0 b 0 A acts on a vector @ y A as follows:
0 0 c
z
0
10
1 0
1
a 0 0
x
ax
@ 0 b 0 A @ y A = @ by A
0 0 c
z
c
Maths 632
Notes on invertible transformations and matrices
April 18, 2008
In class yesterday we proved that a linear transformation T from R3 to R3 is one-to-one if and only if it
is onto. This was done by discussing the two important properties that a se