2 Group 17
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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
∈
ℝ
d)
a
=
-
1
/
4
e)
a
=
-
4
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
=
6
b)
a
=
2
c)
a
=
5
d)
it has a solution for all
a
∈
ℝ
e)
a
=
1
Question 3.
Determine the rank of the matrix
(
1
,
1
,
4
2
,
1
,
1
3
,
1
,
-
2
1
,
5
,
32
)
.
a)
2
b)
4
c)
0
d)
3
e)
1
Evaluate