2 Group 18
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Question 1.
The set of all linear combinations of vectors
u
=
(
2
,
1
)
,
v
=
(
4
,
-
2
)
is
a)
all nonzero multiples of the vector
u
b)
all multiples of the vector
u
c)
all vectors from
ℝ
2
d)
vectors
u
,
v
,
u
+
v
,
u
-
v
e)
all nonzero vectors from
ℝ
2
Question 2.
For which
a
∈
ℝ
has the following system of linear equations a unique solution?
2
x
+
2
y
-
2
z
=
0
x
+
y
+
a
z
=
a
y
+
z
=
a
a)
a
≠
-
1
b)
a
=
3
c)
a
≠
12
d)
a
=
-
1
e)
for all
a
∈
ℝ
Question 3.
Determine the matrix
X
satisfying
5
X
-
2
A
=
E
, if
A
=
(
1
,
2
,
0
-
1
,
0
,
2
3
,
1
,
1
)
.
a)
X
=
(
3
,
4
,
0
-
2
,
1
,
4
6
,
2
,
3
)
b)
X
=
5
(
3
,
5
,
1
-
1
,
2
,
5
7
,
3
,
3
)
c)
X
=
1
5
(
3
,
5
,
1
-
1
,
2
,
5
7
,
3
,
3
)
d)
X
=
1
5
(
3
,
4
,
0
-
2
,
1
,
4
6
,
2
,
3
)
e)
X
=
1
5
(
-
1
,
-
4
,
0
2
,
1
,
-
4
-
6
,
-
2
,
-
1
)
Evaluate