Question 18 - Week 5 Practice | Prasnya
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Week 5
Field
IITM-DS
Exam
Quiz 2
Subject
Mathematics 2
Week
Week 5
Question 18 of 19
Practice question
00:00
Est. 3 min
Marks
+2.00
0.00
Question
Which of the following options are true?
Multiple correct
Medium Difficulty
20 November 2022
A
If
A
A
is a non-zero matrix of order
4
×
3
4\times3
and
rank
(
A
)
=
3
\operatorname{rank}(A)=3
, then the rows of
A
A
are linearly independent.
B
If
A
A
is a non-zero matrix of order
4
×
3
4\times3
and
rank
(
A
)
=
3
\operatorname{rank}(A)=3
, then the columns of
A
A
are linearly independent.
C
If
A
A
is a non-zero matrix of order
m
×
(
m
+
1
)
m\times(m+1)
,
m
>
1
m>1
, then the maximum possible nullity of
A
A
is
m
m
.
D
If
A
A
is a non-zero matrix of order
4
×
5
4\times5
and
rank
(
A
)
=
3
\operatorname{rank}(A)=3
, then the dimension of the solution space of
A
x
=
0
Ax=0
is
2
2
.
