2 Group 4
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Question 1.
The vector
(
a
,
0
,
a
)
is a linear combination of the vectors
(
1
,
1
,
-
2
)
,
(
3
,
1
,
0
)
if and only if
a)
a
=
2
b)
a
≠
0
c)
a
∈
{
0
,
2
}
d)
a
∈
ℝ
e)
a
=
0
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
=
a
a)
a
=
2
b)
a
=
1
c)
it has a solution for all
a
∈
ℝ
d)
a
=
-
1
e)
a
=
3
Question 3.
Determine the rank of the matrix
(
3
,
2
,
1
4
,
-
2
,
4
5
,
8
,
-
1
5
,
-
6
,
7
7
,
-
14
,
13
)
.
a)
4
b)
2
c)
3
d)
0
e)
1
Evaluate