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Question 39 - Week 6 Practice | Prasnya
Q39
00:00
6 Aug 2023
Q39.
Which of the following options are true?
A
There exists an onto linear transformation
T
:
R
3
→
R
2
T:\mathbb{R}^3\to\mathbb{R}^2
T
:
R
3
→
R
2
.
B
There does not exist a one-one linear transformation
T
:
R
3
→
R
T:\mathbb{R}^3\to\mathbb{R}
T
:
R
3
→
R
.
C
There exists a linear transformation
T
:
R
3
→
R
2
T:\mathbb{R}^3\to\mathbb{R}^2
T
:
R
3
→
R
2
such that
rank
(
T
)
=
nullity
(
T
)
\operatorname{rank}(T)=\operatorname{nullity}(T)
rank
(
T
)
=
nullity
(
T
)
.
D
There does not exist a linear transformation
T
:
R
2
→
R
3
T:\mathbb{R}^2\to\mathbb{R}^3
T
:
R
2
→
R
3
such that
rank
(
T
)
=
nullity
(
T
)
\operatorname{rank}(T)=\operatorname{nullity}(T)
rank
(
T
)
=
nullity
(
T
)
.
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Check
Details
Q39
00:00
6 Aug 2023
Q39.
Which of the following options are true?
A
There exists an onto linear transformation
T
:
R
3
→
R
2
T:\mathbb{R}^3\to\mathbb{R}^2
T
:
R
3
→
R
2
.
B
There does not exist a one-one linear transformation
T
:
R
3
→
R
T:\mathbb{R}^3\to\mathbb{R}
T
:
R
3
→
R
.
C
There exists a linear transformation
T
:
R
3
→
R
2
T:\mathbb{R}^3\to\mathbb{R}^2
T
:
R
3
→
R
2
such that
rank
(
T
)
=
nullity
(
T
)
\operatorname{rank}(T)=\operatorname{nullity}(T)
rank
(
T
)
=
nullity
(
T
)
.
D
There does not exist a linear transformation
T
:
R
2
→
R
3
T:\mathbb{R}^2\to\mathbb{R}^3
T
:
R
2
→
R
3
such that
rank
(
T
)
=
nullity
(
T
)
\operatorname{rank}(T)=\operatorname{nullity}(T)
rank
(
T
)
=
nullity
(
T
)
.
Save
Check
Details
