Math 33A
Spring 2008
First midterm exam study guide
The first midterm exam will cover the material from chapters 1–3 in the textbook (this includes Section
3.4, which was covered in lecture on Monday, April 21).
1
Essential notions and techniques
The following is a list of essential notions you should know, and techniques you should be able to use, from
the first three chapters of the textbook.
•
Be able to solve a system of linear equations using GaussJordan elimination;
•
Be able to transform a matrix into reduced rowechelon form;
•
Be able to multiply a matrix with a vector;
•
Be able to find the matrix of a linear transformation, given the values
T
(
~e
1
),
T
(
~e
2
),
. . .
,
T
(
~e
n
), or from
the values
T
(
~v
1
),
T
(
~v
2
),
. . .
,
T
(
~v
n
) for some vectors
~v
i
simplyrelated to the vectors
~e
i
;
•
Be able to determine the rank of an
n
×
m
matrix;
•
Know how the rank of an
n
×
m
coefficient matrix relates to the number of solutions that the corre
sponding system has;
•
Know that a function
T
from
R
m
to
R
n
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 Spring '08
 lee
 Math, Linear Algebra, Vector Space, linear transformation

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