Problem 1Draw u = 41" , w = −22" and (u + w), (u − w) in the
plane.
1
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.
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3
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fProblem 2 Find vectors u and w such that u + w = 2
4
4
5
6
3
5 and
u − w = 2
4
2
5
8
3
5.
2
Cut wt
t
Cu
-
w
)
=
[%)
⇒
su
-
-
LIED
⇒
u
-
-
EH
w
-
-
Est Est
.Problem 3
] Find two vectors u and w which are perpendicular
to 2
4
1
0
13
5 and to each other.
3
Let
u
-
-
I and
w
-
-
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U
.
[E)
= o
⇒ 21*23=0
w
.
[I]=o
⇒
bath3=0
u
.
W
-
-
o
⇒
Tebet22/021-73/03=0
Choose randomly
I
,
-23=0
Then
bat bz=o & 72102=0
Since
we don't want the trivial
vector
we choose 22--1,102=0
and 101--1,103=-1 u.IE] ,w=[Is]Problem 4 [20pts] How long is the vector u = 2
6
6
6
6
4
1
1
1
1
1
3
7
7
7
7
5
?
4
Hull
=
Iie
=
FsProblem 5 Consider the following system of equations: 8
>
<
>
:
2
x
+ 3
y
+
z
= 8
4
x
+ 7
y
+ 5
z
= 20
−
2y
+ 2
z
= 0
(i) Apply Gauss Elimination in order to solve it;
(ii) Transform the above system of equations in matrix form and apply the
Gauss Elimination in matrix form (indicate all matrices you used in
the process).
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⑤ 2
=
8
Z =L ,
y
=
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, X
=
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