Question 28 - Week 4 Practice | Prasnya
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Week 4
Question 28
00:00
Est. 3 min
Marks:
+3.00
0.00
Consider the following subsets of
R
4
\mathbb{R}^4
.
W
=
span
{
(
2
,
−
1
,
0
,
4
)
,
(
−
1
,
1
,
0
,
3
)
,
(
1
,
2
,
0
,
3
)
,
(
2
,
2
,
0
,
10
)
}
W=\operatorname{span}\{(2,-1,0,4),(-1,1,0,3),(1,2,0,3),(2,2,0,10)\}
,
B
1
=
{
(
1
,
0
,
0
,
0
)
,
(
0
,
1
,
0
,
0
)
,
(
0
,
0
,
0
,
1
)
}
B_1=\{(1,0,0,0),(0,1,0,0),(0,0,0,1)\}
, and
B
2
=
{
(
2
,
−
1
,
0
,
4
)
,
(
−
1
,
1
,
0
,
3
)
,
(
1
,
2
,
0
,
3
)
}
B_2=\{(2,-1,0,4),(-1,1,0,3),(1,2,0,3)\}
. Select the correct option.
Single correct
Medium Difficulty
07 July 2024
A
Both
B
1
B_1
and
B
2
B_2
are bases for
W
W
.
B
B
1
B_1
is a basis for
W
W
, but
B
2
B_2
is not.
C
B
2
B_2
is a basis for
W
W
, but
B
1
B_1
is not.
D
Neither
B
1
B_1
nor
B
2
B_2
is a basis for
W
W
.
