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Question 9 - Week 5 Practice | Prasnya
Q9
00:00
4 Aug 2024
Q9.
Select all true statements.
A
For a matrix
A
A
A
of dimensions
m
×
n
m\times n
m
×
n
, the rank of the matrix is equal to
min
{
m
,
n
}
\min\{m,n\}
min
{
m
,
n
}
.
B
The nullity of an invertible matrix is always zero.
C
For a matrix
A
A
A
of dimensions
m
×
n
m\times n
m
×
n
, the row space of
A
A
A
is the same as the column space of
A
A
A
.
D
If
A
A
A
and
B
B
B
are square matrices of order
n
n
n
such that
rank
(
A
B
)
=
n
\operatorname{rank}(AB)=n
rank
(
A
B
)
=
n
, then both
A
A
A
and
B
B
B
must be invertible.
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Details
Q9
00:00
4 Aug 2024
Q9.
Select all true statements.
A
For a matrix
A
A
A
of dimensions
m
×
n
m\times n
m
×
n
, the rank of the matrix is equal to
min
{
m
,
n
}
\min\{m,n\}
min
{
m
,
n
}
.
B
The nullity of an invertible matrix is always zero.
C
For a matrix
A
A
A
of dimensions
m
×
n
m\times n
m
×
n
, the row space of
A
A
A
is the same as the column space of
A
A
A
.
D
If
A
A
A
and
B
B
B
are square matrices of order
n
n
n
such that
rank
(
A
B
)
=
n
\operatorname{rank}(AB)=n
rank
(
A
B
)
=
n
, then both
A
A
A
and
B
B
B
must be invertible.
Save
Check
Details
