Question 3 - Week 4 Practice | Prasnya
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Week 4
Field
IITM-DS
Exam
Quiz 2
Subject
Mathematics 2
Week
Week 4
Question 3 of 7
Practice question
00:00
Est. 3 min
Marks
+2.00
0.00
Question
Select all true statements.
Multiple correct
Medium Difficulty
24 March 2024
A
A
A
and
B
B
are square matrices of order
n
n
. If
rank
(
A
)
=
k
\operatorname{rank}(A)=k
, with
k
≤
n
k\le n
, and
rank
(
B
)
=
n
\operatorname{rank}(B)=n
, then
rank
(
A
B
)
=
k
\operatorname{rank}(AB)=k
.
B
The rank of a matrix is equal to the maximum number of linearly independent columns.
C
The rank of a diagonal matrix is equal to the number of diagonal entries that are zero.
D
For a matrix
A
A
of dimensions
m
×
n
m\times n
,
rank
(
A
)
+
nullity
(
A
)
=
m
\operatorname{rank}(A)+\operatorname{nullity}(A)=m
.
