2 Group 7
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Question 1.
The vector
(
a
,
-
1
)
is a linear combination of the vectors
(
1
,
4
)
,
(
-
4
,
-
16
)
if and only if
a)
a
=
4
b)
a
=
1
/
4
c)
a
=
-
4
d)
a
=
-
1
/
4
e)
a
∈
ℝ
Question 2.
For which
a
∈
ℝ
has the following system of linear equations no solution?
2
x
+
2
y
-
2
z
=
0
x
+
y
+
a
z
=
a
y
+
z
=
a
a)
a
=
1
b)
a
=
3
c)
a
=
-
1
d)
it has a solution for all
a
∈
ℝ
e)
a
=
-
2
Question 3.
Determine the matrix
X
satisfying
5
B
+
X
=
2
A
, if
A
=
(
1
,
-
3
,
2
0
,
4
,
1
1
,
-
1
,
0
)
,
B
=
(
0
,
2
,
-
1
4
,
-
5
,
0
1
,
-
2
,
1
)
.
a)
X
=
(
2
,
4
,
-
1
20
,
-
17
,
2
7
,
-
12
,
5
)
b)
X
=
(
1
,
-
1
,
1
4
,
-
1
,
1
2
,
-
3
,
1
)
c)
X
=
(
2
,
-
16
,
9
-
20
,
33
,
2
-
3
,
8
,
-
5
)
d)
X
=
(
2
,
-
8
,
5
-
4
,
13
,
2
1
,
1
,
-
1
)
e)
X
=
(
1
,
-
13
,
7
-
20
,
29
,
1
-
4
,
9
,
-
5
)
Evaluate