2 Group 5
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Question 1.
The vector
(
0
,
a
,
-
3
)
is a linear combination of the vectors
(
1
,
2
,
-
1
)
,
(
4
,
2
,
2
)
if and only if
a)
a
≠
0
b)
a
≠
3
c)
a
∈
ℝ
d)
a
∈
{
0
,
3
}
e)
a
=
3
Question 2.
For which
a
∈
ℝ
has the following system a unique solution?
x
+
y
-
z
=
0
2
x
+
2
y
+
a
z
=
a
y
+
z
=
a
a)
a
=
-
2
b)
a
≠
11
c)
for all
a
∈
ℝ
d)
a
=
5
e)
a
≠
-
2
Question 3.
Determine the rank of the matrix
(
6
,
-
5
,
1
,
0
2
,
1
,
-
1
,
2
3
,
0
,
2
,
1
1
,
-
6
,
-
2
,
1
1
,
-
7
,
1
,
1
)
.
a)
1
b)
2
c)
4
d)
0
e)
3
Evaluate