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Question 3 - Week 7 Practice | Prasnya
Q3
00:00
6 Apr 2026
Q3.
Let
A
A
A
and
B
B
B
be square matrices of the same order
n
n
n
. Which statements are sufficient to conclude that
A
A
A
is equivalent to
B
B
B
?
A
det
(
A
)
=
det
(
B
)
\det(A)=\det(B)
det
(
A
)
=
det
(
B
)
.
B
nullity
(
A
)
=
nullity
(
B
)
\operatorname{nullity}(A)=\operatorname{nullity}(B)
nullity
(
A
)
=
nullity
(
B
)
.
C
The set of columns of
A
A
A
and the set of columns of
B
B
B
are both linearly dependent subsets of
R
n
\mathbb{R}^n
R
n
.
D
There exists a matrix
C
C
C
such that
A
A
A
is equivalent to
C
C
C
, and
B
B
B
is equivalent to
C
C
C
.
E
There exist invertible matrices
P
P
P
and
Q
Q
Q
of order
n
n
n
such that
P
A
=
B
Q
PA=BQ
P
A
=
B
Q
.
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Details
Q3
00:00
6 Apr 2026
Q3.
Let
A
A
A
and
B
B
B
be square matrices of the same order
n
n
n
. Which statements are sufficient to conclude that
A
A
A
is equivalent to
B
B
B
?
A
det
(
A
)
=
det
(
B
)
\det(A)=\det(B)
det
(
A
)
=
det
(
B
)
.
B
nullity
(
A
)
=
nullity
(
B
)
\operatorname{nullity}(A)=\operatorname{nullity}(B)
nullity
(
A
)
=
nullity
(
B
)
.
C
The set of columns of
A
A
A
and the set of columns of
B
B
B
are both linearly dependent subsets of
R
n
\mathbb{R}^n
R
n
.
D
There exists a matrix
C
C
C
such that
A
A
A
is equivalent to
C
C
C
, and
B
B
B
is equivalent to
C
C
C
.
E
There exist invertible matrices
P
P
P
and
Q
Q
Q
of order
n
n
n
such that
P
A
=
B
Q
PA=BQ
P
A
=
B
Q
.
Save
Check
Details
