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Question 12 - Week 3 Practice | Prasnya
Q12
00:00
7 Jul 2024
Q12.
B
=
{
v
1
,
v
2
,
v
3
}
B=\{v_1,v_2,v_3\}
B
=
{
v
1
,
v
2
,
v
3
}
is a linearly independent subset of
R
3
\mathbb{R}^3
R
3
. Select all linearly independent subsets of
R
3
\mathbb{R}^3
R
3
from the following.
A
{
v
1
+
v
2
,
v
1
−
v
2
}
\{v_1+v_2, v_1-v_2\}
{
v
1
+
v
2
,
v
1
−
v
2
}
B
{
v
1
,
v
2
,
v
3
,
v
4
}
\{v_1,v_2,v_3,v_4\}
{
v
1
,
v
2
,
v
3
,
v
4
}
, where
v
4
v_4
v
4
is some vector in
R
3
\mathbb{R}^3
R
3
C
{
v
1
+
v
2
,
v
1
−
v
2
,
v
1
+
v
2
+
v
3
}
\{v_1+v_2, v_1-v_2, v_1+v_2+v_3\}
{
v
1
+
v
2
,
v
1
−
v
2
,
v
1
+
v
2
+
v
3
}
D
{
v
1
,
v
1
+
v
2
,
v
1
−
v
2
}
\{v_1, v_1+v_2, v_1-v_2\}
{
v
1
,
v
1
+
v
2
,
v
1
−
v
2
}
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Q12
00:00
7 Jul 2024
Q12.
B
=
{
v
1
,
v
2
,
v
3
}
B=\{v_1,v_2,v_3\}
B
=
{
v
1
,
v
2
,
v
3
}
is a linearly independent subset of
R
3
\mathbb{R}^3
R
3
. Select all linearly independent subsets of
R
3
\mathbb{R}^3
R
3
from the following.
A
{
v
1
+
v
2
,
v
1
−
v
2
}
\{v_1+v_2, v_1-v_2\}
{
v
1
+
v
2
,
v
1
−
v
2
}
B
{
v
1
,
v
2
,
v
3
,
v
4
}
\{v_1,v_2,v_3,v_4\}
{
v
1
,
v
2
,
v
3
,
v
4
}
, where
v
4
v_4
v
4
is some vector in
R
3
\mathbb{R}^3
R
3
C
{
v
1
+
v
2
,
v
1
−
v
2
,
v
1
+
v
2
+
v
3
}
\{v_1+v_2, v_1-v_2, v_1+v_2+v_3\}
{
v
1
+
v
2
,
v
1
−
v
2
,
v
1
+
v
2
+
v
3
}
D
{
v
1
,
v
1
+
v
2
,
v
1
−
v
2
}
\{v_1, v_1+v_2, v_1-v_2\}
{
v
1
,
v
1
+
v
2
,
v
1
−
v
2
}
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Check
Details
