2 Group 15
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Question 1.
The vector
(
7
,
0
)
is a linear combination of the vectors
(
-
2
,
1
)
,
(
4
,
b
)
if and only if
a)
b
≠
-
2
b)
b
=
0
c)
b
∈
ℝ
d)
b
=
2
e)
b
=
-
2
Question 2.
For which
a
∈
ℝ
has the following system of linear equations no solution?
x
+
y
-
z
=
0
2
x
+
2
y
+
a
z
=
a
-
y
-
z
=
2
a
a)
it has a solution for all
a
∈
ℝ
b)
a
=
3
c)
a
=
2
d)
a
=
-
2
e)
a
=
1
Question 3.
Determine the matrix
X
satisfying
2
(
1
3
X
+
2
A
)
=
X
-
B
, if
A
=
(
1
,
2
-
2
,
0
)
,
B
=
(
-
1
,
-
7
6
,
2
)
.
a)
X
=
(
-
2
,
-
9
8
,
2
)
b)
X
=
(
15
,
43
-
42
,
-
6
)
c)
X
=
(
9
,
3
-
6
,
6
)
d)
X
=
(
-
5
,
-
1
14
,
2
)
e)
X
=
(
-
3
,
-
1
-
2
,
2
)
Evaluate