2 Group 6
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Question 1.
The vector
(
a
,
0
,
2
a
)
is a linear combination of the vectors
(
1
,
1
,
-
2
)
,
(
4
,
2
,
-
2
)
if and only if
a)
a
∈
{
0
,
4
}
b)
a
≠
0
c)
a
=
0
d)
a
=
4
e)
a
∈
ℝ
Question 2.
For which
a
∈
ℝ
has the following system of linear equations no solution?
x
-
2
y
+
2
z
=
0
3
x
-
6
y
+
a
z
=
a
y
+
2
z
=
a
a)
a
=
1
b)
a
=
2
c)
a
=
6
d)
it has a solution for all
a
∈
ℝ
e)
a
=
5
Question 3.
Determine the matrix
X
satisfying
4
(
1
2
X
+
A
)
=
X
-
2
B
, if
A
=
(
2
,
1
5
,
3
)
,
B
=
(
-
1
,
2
1
,
-
2
)
.
a)
X
=
(
3
,
4
-
2
,
1
)
b)
X
=
(
-
10
,
0
-
18
,
-
16
)
c)
X
=
1
3
(
-
6
,
-
8
-
22
,
-
8
)
d)
X
=
(
-
6
,
-
8
-
22
,
-
8
)
e)
X
=
(
6
,
8
22
,
8
)
Evaluate