Problem 1
a)
xQx
[x][b][]
=
Ex < 2]
=
2x
2
=
f(x)
x,
=
x,
,
+
,
x (x + 4x2)
,
2x , + 4x
2
+ x , x2 +
2
+ x , x2 +
2x ?
2x2 + x + 2x
,
b)
2)
*f=
[2 ]
Q
=
[2][] [iii]
=
b + Qx
=
=
[2) + [ ]
[
=
Of
,
Problem 2
1)
II VII
E
=
viw
=
cost
,
I wil
=
0
=
E
2
=
Fo
,
arcos
(b)
so
[ii]
x + 2x -
,
,
=
=
[12]
2x, + < 2+ x 3 + 4x
=
[xTQx
=
/
[2 i ]
( , (2x ,+ >(2) +
=
bi
verited
2) Letm W
V
IV wI
=
.
of
norm
VII
3) Equal
VI1 n
and
.
1 will v ul
.
smaller
is
when
or
(1 2) & (2 4)
are
dot product
10
,
,
is
(1 2) & (2 3)
dot product is
4)
if
8
Viw 30
Viw O
,
ViW
(1)
(2) Viw
=
(3) viw
=
linearly dependent
product of norms
so
acute
,
so
right
-12 , so
w
(a
viw
=
IIVII
=
,
,
c)
impose
,
a+ C
V
,
11011
a2+ b2 + c
E
b
=
0
=
=
is
F
.
v3
=
=
Noo
=
10
55
obtuse
,
b
.
angle
=
=
55 50
,
5) v (1 0 1)
,
is
obtuse
,
O
of
linearly dependent
are
norms
Since
right
,
1
=
rorm
to
,
acute
=
viw <O
1 will Vill < I wllVII
w
product
,
then
,
so ,
independent
linearly
of
are
,
.
,
=
equal
&
v
If
.
V = V + U1
.
,
(v u) u
=
on w
unit rector
the
=
↑
UWIl
=
1
a+ b+ c
1
for simplicity
w
(a+ c)2
=
a+ 2ac + c
=
=
ac =
Since
a, c
-t
E
& product I
roots of
Exx
sum
are
1 + 2ac
is
-
2
-
=+
2
1
= ,)
0
Problem 3
Results
and
Discussion
ipynb
in