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Question 38 - Week 8 Practice | Prasnya
Q38
00:00
20 Nov 2022
Q38.
Which of the following options are true?
@passage
A
For all
v
∈
V
v\in V
v
∈
V
,
v
−
P
W
(
v
)
v-P_W(v)
v
−
P
W
(
v
)
is orthogonal to
W
W
W
.
B
If
dim
(
W
)
=
2
\dim(W)=2
dim
(
W
)
=
2
, then the dimension of the null space of
P
W
P_W
P
W
may not be
1
1
1
.
C
The zero vector is orthogonal to every vector of
V
V
V
.
D
If
v
∈
W
v\in W
v
∈
W
, then
P
W
(
v
)
=
v
P_W(v)=v
P
W
(
v
)
=
v
.
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Q38
00:00
20 Nov 2022
Q38.
Which of the following options are true?
@passage
A
For all
v
∈
V
v\in V
v
∈
V
,
v
−
P
W
(
v
)
v-P_W(v)
v
−
P
W
(
v
)
is orthogonal to
W
W
W
.
B
If
dim
(
W
)
=
2
\dim(W)=2
dim
(
W
)
=
2
, then the dimension of the null space of
P
W
P_W
P
W
may not be
1
1
1
.
C
The zero vector is orthogonal to every vector of
V
V
V
.
D
If
v
∈
W
v\in W
v
∈
W
, then
P
W
(
v
)
=
v
P_W(v)=v
P
W
(
v
)
=
v
.
Save
Read
Check
Details
