2 Group 20
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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
≠
0
b)
a
=
8
c)
a
=
-
8
d)
a
∈
ℝ
e)
a
≠
-
6
Question 2.
For which
a
∈
ℝ
has the following system of linear equations a unique solution?
2
x
+
y
+
z
=
0
4
x
+
2
y
+
a
z
=
a
y
+
2
z
=
a
a)
a
=
1
b)
a
≠
1
c)
for all
a
∈
ℝ
d)
a
≠
2
e)
a
=
4
Question 3.
Determine the rank of the matrix
(
1
,
2
,
-
2
,
-
1
2
,
-
3
,
1
,
1
1
,
9
,
-
7
,
-
4
)
.
a)
3
b)
2
c)
0
d)
4
e)
1
Evaluate