2 Group 2
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Question 1.
The vector
(
a
,
3
)
is a linear combination of the vectors
(
-
2
,
4
)
,
(
1
,
-
2
)
if and only if
a)
a
=
-
2
/
3
b)
a
=
-
3
/
2
c)
a
∈
ℝ
d)
a
=
3
e)
a
=
-
3
Question 2.
For which
a
∈
ℝ
has the following system of linear equations no solution?
2
x
+
y
+
z
=
0
4
x
+
2
y
+
a
z
=
a
y
+
2
z
=
a
a)
a
=
3
b)
a
=
1
c)
it has a solution for all
a
∈
ℝ
d)
a
=
-
1
e)
a
=
2
Question 3.
Determine the rank of the matrix
(
3
,
2
,
1
4
,
-
2
,
4
5
,
8
,
-
1
5
,
-
6
,
7
7
,
-
14
,
13
)
.
a)
2
b)
4
c)
0
d)
1
e)
3
Evaluate