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Question 15 - Week 3 Practice | Prasnya
Q15
00:00
25 Feb 2024
Q15.
Which of the following is/are correct?
@passage
A
V
V
V
has no zero element with respect to the given addition.
B
(
0
,
0
,
0
)
(0,0,0)
(
0
,
0
,
0
)
is the zero element of
V
V
V
with respect to the given addition.
C
(
0
,
0
,
5
)
(0,0,5)
(
0
,
0
,
5
)
is the zero element of
V
V
V
with respect to the given addition.
D
For any real number
c
c
c
, we always have
c
(
0
,
1
,
5
)
=
(
0
,
1
,
5
)
c(0,1,5)=(0,1,5)
c
(
0
,
1
,
5
)
=
(
0
,
1
,
5
)
.
E
For each element
v
∈
V
v\in V
v
∈
V
and for each pair
a
,
b
∈
R
a,b\in\mathbb{R}
a
,
b
∈
R
,
(
a
+
b
)
v
=
a
v
+
b
v
(a+b)v=av+bv
(
a
+
b
)
v
=
a
v
+
b
v
.
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Details
Q15
00:00
25 Feb 2024
Q15.
Which of the following is/are correct?
@passage
A
V
V
V
has no zero element with respect to the given addition.
B
(
0
,
0
,
0
)
(0,0,0)
(
0
,
0
,
0
)
is the zero element of
V
V
V
with respect to the given addition.
C
(
0
,
0
,
5
)
(0,0,5)
(
0
,
0
,
5
)
is the zero element of
V
V
V
with respect to the given addition.
D
For any real number
c
c
c
, we always have
c
(
0
,
1
,
5
)
=
(
0
,
1
,
5
)
c(0,1,5)=(0,1,5)
c
(
0
,
1
,
5
)
=
(
0
,
1
,
5
)
.
E
For each element
v
∈
V
v\in V
v
∈
V
and for each pair
a
,
b
∈
R
a,b\in\mathbb{R}
a
,
b
∈
R
,
(
a
+
b
)
v
=
a
v
+
b
v
(a+b)v=av+bv
(
a
+
b
)
v
=
a
v
+
b
v
.
Save
Read
Check
Details
