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Question 40 - Week 6 Practice | Prasnya
Q40
00:00
6 Aug 2023
Q40.
Consider
V
=
{
[
a
b
&
¸
a
]
:
c
=
a
+
b
;
a
,
b
,
c
∈
R
}
V=\left\{\begin{bmatrix}a&b\c\&a\end{bmatrix}:c=a+b;\ a,b,c\in\mathbb{R}\right\}
V
=
{
[
a
b
&
¸
a
]
:
c
=
a
+
b
;
a
,
b
,
c
∈
R
}
and
T
:
V
→
R
4
T:V\to\mathbb{R}^4
T
:
V
→
R
4
defined by
T
(
A
)
=
(
a
,
b
,
c
,
a
+
b
−
c
)
T(A)=(a,b,c,a+b-c)
T
(
A
)
=
(
a
,
b
,
c
,
a
+
b
−
c
)
. Choose the correct options.
A
T
T
T
is onto but not one-one.
B
T
T
T
is one-one but not onto.
C
The nullspace of
T
T
T
is a
2
2
2
-dimensional subspace of
V
V
V
.
D
The range of
T
T
T
is a
2
2
2
-dimensional subspace of
R
4
\mathbb{R}^4
R
4
.
Save
Check
Details
Q40
00:00
6 Aug 2023
Q40.
Consider
V
=
{
[
a
b
&
¸
a
]
:
c
=
a
+
b
;
a
,
b
,
c
∈
R
}
V=\left\{\begin{bmatrix}a&b\c\&a\end{bmatrix}:c=a+b;\ a,b,c\in\mathbb{R}\right\}
V
=
{
[
a
b
&
¸
a
]
:
c
=
a
+
b
;
a
,
b
,
c
∈
R
}
and
T
:
V
→
R
4
T:V\to\mathbb{R}^4
T
:
V
→
R
4
defined by
T
(
A
)
=
(
a
,
b
,
c
,
a
+
b
−
c
)
T(A)=(a,b,c,a+b-c)
T
(
A
)
=
(
a
,
b
,
c
,
a
+
b
−
c
)
. Choose the correct options.
A
T
T
T
is onto but not one-one.
B
T
T
T
is one-one but not onto.
C
The nullspace of
T
T
T
is a
2
2
2
-dimensional subspace of
V
V
V
.
D
The range of
T
T
T
is a
2
2
2
-dimensional subspace of
R
4
\mathbb{R}^4
R
4
.
Save
Check
Details
