2 Group 8
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Question 1.
The vector
(
0
,
2
b
,
-
5
)
is a linear combination of the vectors
(
2
,
-
2
,
4
)
,
(
5
,
1
,
4
)
if and only if
a)
b
=
5
/
2
b)
b
=
0
c)
b
≠
0
d)
b
∈
ℝ
e)
b
=
5
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)
a
=
-
2
b)
a
=
2
c)
a
=
3
d)
it has a solution for all
a
∈
ℝ
e)
a
=
1
Question 3.
Determine the rank of the matrix
(
3
,
2
,
1
4
,
-
2
,
4
6
,
4
,
2
9
,
6
,
3
)
.
a)
1
b)
2
c)
3
d)
4
e)
0
Evaluate