Question 35 - Week 4 Practice | Prasnya
Prasnya
Continue with Google
Practice path
Dashboard
Exam
Qualifier / Quiz 1
Go to subject
Mathematics 2
Go to chapter
Week 4
Question 35
00:00
Est. 3 min
Marks:
+3.00
0.00
Passage
Let
W
1
=
{
(
x
,
y
,
z
)
∈
R
3
:
2
x
−
y
+
z
=
0
}
W_1=\{(x,y,z)\in\mathbb{R}^3:2x-y+z=0\}
,
W
2
=
{
(
x
,
y
,
z
)
∈
R
3
:
2
x
−
y
+
z
=
0
,
2
x
+
y
−
3
z
=
0
}
W_2=\{(x,y,z)\in\mathbb{R}^3:2x-y+z=0,\;2x+y-3z=0\}
, and let
W
3
W_3
be the
x
y
xy
-plane. Based on the above data, answer the given subquestions.
Question
Choose the correct option(s) from the following statements.
Comprehension
Medium Difficulty
29 October 2023
A
The set
{
(
1
,
0
,
−
2
)
,
(
0
,
1
,
1
)
}
\{(1,0,-2),(0,1,1)\}
forms a basis for
W
1
W_1
.
B
W
2
W_2
is the set of all solutions of the system
A
X
=
0
AX=0
, where
A
=
[
2
2
−
1
1
1
−
3
]
A=\begin{bmatrix}2&2\\-1&1\\1&-3\end{bmatrix}
.
C
The intersection of
W
1
W_1
and
W
3
W_3
is the line
y
=
2
x
y=2x
.
D
The intersection of
W
1
W_1
and
W
2
W_2
is spanned by the vector
(
2
,
1
,
0
)
(2,1,0)
.
E
W
2
W_2
is the straight line in
R
3
\mathbb{R}^3
passing through the origin and the vector
(
1
,
4
,
2
)
(1,4,2)
.