Definitions
2.3
•
If S = {
v
1
, v
2
, …, v
k
}
is a set of vectors in R
n
, then the set of all linear combinations of
v
1
,
v
2
, …, v
k
is called the
span
of
v
1
, v
2
, …, v
k
and is denoted by span(
v
1
, v
2
, …, v
k
) or
span(S).
If span(S) = R
n
, then S is called a
spanning set
for R
n
.
•
A set of vectors
v
1
, v
2
, …, v
k
is
linearly dependent
if there are scalars c
1
, c
2
, …, c
k
, at
least one of which is not zero, such that: c
1
v
1
+c
2
v
2
+
…
+c
k
v
k
=
0
.
A set of vectors that is not
linearly dependent is called
linearly independent
.
2.2
•
A system of linear equations is called
homogeneous
if the constant term in each equation
is zero.
•
A matrix is in
reduced row echelon
form if it satisfies the following properties.
1.
It is in row echelon form.
2.
The leading entry in each nonzero row is a 1 (called a
leading 1
).
3.
Each column containing a leading 1 has zeros everywhere else.
•
The
rank
of a matrix is the number of nonzero rows in its row echelon form.
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 Spring '08
 Yeap
 Linear Algebra, Algebra, Vectors, Row echelon form, Proju

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