1
Math 2331 HW 1 Key
Problem:
If
° = ±
1
3
5
²
,
³ = ±
1
1
1
²
,
´ = ±
1
1
−2
²
µ = ±
1
0
0
²
,
¶ = ±
0
1
0
²
,
· = ±
0
0
1
²
a)
° ∙ µ = ¸. ¸ + ¹. º + ». º = ¸
b)
° ∙ ³ = ¸. ¸ + ¹. ¸ + ». ¸ = ¼
c) Express
°
and
´
as a linear combination of
µ, ¶
and
·
:
° = ¸µ + ¹¶ + »·
´ = ¸µ + ¸¶ − ½·
d) Length of
° = √¸
½
+ ¹
½
+ »
½
= √¹»
.
e) Length of
° + ½´ = √¹
½
+ »
½
+ ¸
½
= √¹»
since
3
2
5
1
v
u
+
=
.
f) What is the cosine of the angle between
°
and
³
? Are they perpendicular?
9
3 105
cos( )
35
35
3
v w
v
w
θ
=
=
=
i
No, not perpendicular since
cos( )
0
θ
≠
.
g) Use given vectors to fill in:
__
i
___ and
__
j
___ are perpendicular to each other.
__
i
___ and
__
k
___ are perpendicular to each other.
__
j
___ and
__
k
___ are perpendicular to each other.
___
u
__ and
__
w
___ are perpendicular to each other.
h) Give a vector that is perpendicular to
°
.
3
0
1
, 5
,...
0
3


i) Give a vector that is perpendicular to
° + ³
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Staff
 Math, Linear Algebra, Algebra, Vector Space, Linear combination, vw

Click to edit the document details