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Question 3 - Week 4 Practice | Prasnya
Q3
00:00
24 Mar 2024
Q3.
Select all true statements.
A
A
A
A
and
B
B
B
are square matrices of order
n
n
n
. If
rank
(
A
)
=
k
\operatorname{rank}(A)=k
rank
(
A
)
=
k
, with
k
≤
n
k\le n
k
≤
n
, and
rank
(
B
)
=
n
\operatorname{rank}(B)=n
rank
(
B
)
=
n
, then
rank
(
A
B
)
=
k
\operatorname{rank}(AB)=k
rank
(
A
B
)
=
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
A
of dimensions
m
×
n
m\times n
m
×
n
,
rank
(
A
)
+
nullity
(
A
)
=
m
\operatorname{rank}(A)+\operatorname{nullity}(A)=m
rank
(
A
)
+
nullity
(
A
)
=
m
.
Save
Check
Details
Q3
00:00
24 Mar 2024
Q3.
Select all true statements.
A
A
A
A
and
B
B
B
are square matrices of order
n
n
n
. If
rank
(
A
)
=
k
\operatorname{rank}(A)=k
rank
(
A
)
=
k
, with
k
≤
n
k\le n
k
≤
n
, and
rank
(
B
)
=
n
\operatorname{rank}(B)=n
rank
(
B
)
=
n
, then
rank
(
A
B
)
=
k
\operatorname{rank}(AB)=k
rank
(
A
B
)
=
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
A
of dimensions
m
×
n
m\times n
m
×
n
,
rank
(
A
)
+
nullity
(
A
)
=
m
\operatorname{rank}(A)+\operatorname{nullity}(A)=m
rank
(
A
)
+
nullity
(
A
)
=
m
.
Save
Check
Details
