2 Group 19
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Question 1.
The vector
(
1
,
-
2
)
is a linear combination of the vectors
(
-
2
,
3
)
,
(
4
,
a
)
if and only if
a)
a
∈
ℝ
b)
a
≠
0
c)
a
≠
-
6
d)
a
=
-
8
e)
a
=
8
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 rank of the matrix
(
1
,
-
3
,
2
,
6
1
,
5
,
8
,
16
0
,
0
,
2
,
-
1
)
.
a)
2
b)
4
c)
0
d)
1
e)
3
Evaluate