2 Group 12
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Question 1.
The vector
(
2
b
,
0
,
b
)
is a linear combination of the vectors
(
-
2
,
-
2
,
4
)
,
(
2
,
1
,
-
1
)
if and only if
a)
b
=
0
b)
b
∈
ℝ
c)
b
∈
{
0
,
1
}
d)
b
=
1
e)
b
≠
0
Question 2.
For which
a
∈
ℝ
has the following system of linear equations a unique solution?
x
+
y
-
z
=
0
2
x
+
2
y
+
a
z
=
a
y
+
z
=
a
a)
a
=
5
b)
a
≠
11
c)
a
=
-
2
d)
a
≠
-
2
e)
for all
a
∈
ℝ
Question 3.
Determine the rank of the matrix
(
1
,
2
,
3
-
4
,
5
,
-
6
7
,
-
8
,
9
10
,
11
,
12
14
,
15
,
16
)
.
a)
0
b)
4
c)
1
d)
2
e)
3
Evaluate