(recall)
Let
v
1
,
v
2
, . . . ,
v
k
be some vectors in R
n
.
A vector
v
in
R
n
is called a linear
combination of
v
1
,
v
2
, . . . ,
v
k
if
v
=
c
1
v
1
+ c
2
v
2
+ . . .
+ c
k
v
k
for some real numbers (scalars)
c
1
,
c
2
, . . . ,
c
k
→
→
→
→
→ →
→
→
→
→
→
Sec 4.2.REV
Monday, February 15, 2010
10:15 PM
Section4dot2REV Page 1

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(recall)
Let
v
1
,
v
2
, . . . ,
v
k
be some vectors in R
n
.
A vector
v
in
R
n
is called a linear
combination of
v
1
,
v
2
, . . . ,
v
k
if
v
=
c
1
v
1
+ c
2
v
2
+ . . .
+ c
k
v
k
for some real numbers (scalars)
c
1
,
c
2
, . . . ,
c
k
Observe that
- 2
v
1
+ 3
v
2
=
- 2 ( 3, 12, - 2 ) + 3 ( 4, - 7, 3 )
=
( - 6, - 24, 4 ) + ( 12, - 21, 9 )
=
(6, - 45, 13 ) =
v
Hence
v
is a linear combination of
v
1
and
v
2
→
→
→
→
→ →
→
→
→
→
→
→
→
→
→
→
→
4.2.REV.1
Monday, February 15, 2010
10:15 PM
Section4dot2REV Page 2