Question 39 - Week 6 Practice | Prasnya
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Week 6
Field
IITM-DS
Exam
Quiz 2
Subject
Mathematics 2
Week
Week 6
Question 39 of 62
Practice question
00:00
Est. 2 min
Marks
+2.00
0.00
Question
Which of the following options are true?
Multiple correct
Medium Difficulty
06 August 2023
A
There exists an onto linear transformation
T
:
R
3
→
R
2
T:\mathbb{R}^3\to\mathbb{R}^2
.
B
There does not exist a one-one linear transformation
T
:
R
3
→
R
T:\mathbb{R}^3\to\mathbb{R}
.
C
There exists a linear transformation
T
:
R
3
→
R
2
T:\mathbb{R}^3\to\mathbb{R}^2
such that
rank
(
T
)
=
nullity
(
T
)
\operatorname{rank}(T)=\operatorname{nullity}(T)
.
D
There does not exist a linear transformation
T
:
R
2
→
R
3
T:\mathbb{R}^2\to\mathbb{R}^3
such that
rank
(
T
)
=
nullity
(
T
)
\operatorname{rank}(T)=\operatorname{nullity}(T)
.
