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Question 26 - Week 7 Practice | Prasnya
Q26
00:00
3 Dec 2023
Q26.
Let
A
A
A
and
B
B
B
be
n
×
n
n\times n
n
×
n
matrices. Which statements are true?
A
If
A
A
A
and
B
B
B
are similar, then the nullity of
A
A
A
and the nullity of
B
B
B
are equal.
B
Let
A
A
A
and
B
B
B
be similar matrices. Then
A
x
=
0
Ax=0
A
x
=
0
has a unique solution if and only if
B
x
=
0
Bx=0
B
x
=
0
has a unique solution.
C
If
A
k
A^k
A
k
and
B
k
B^k
B
k
are similar for some positive integer
k
k
k
, then
A
A
A
and
B
B
B
are similar.
D
If
A
A
A
and
B
B
B
are similar matrices where
A
A
A
is a scalar matrix, then
A
=
B
A=B
A
=
B
.
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Details
Q26
00:00
3 Dec 2023
Q26.
Let
A
A
A
and
B
B
B
be
n
×
n
n\times n
n
×
n
matrices. Which statements are true?
A
If
A
A
A
and
B
B
B
are similar, then the nullity of
A
A
A
and the nullity of
B
B
B
are equal.
B
Let
A
A
A
and
B
B
B
be similar matrices. Then
A
x
=
0
Ax=0
A
x
=
0
has a unique solution if and only if
B
x
=
0
Bx=0
B
x
=
0
has a unique solution.
C
If
A
k
A^k
A
k
and
B
k
B^k
B
k
are similar for some positive integer
k
k
k
, then
A
A
A
and
B
B
B
are similar.
D
If
A
A
A
and
B
B
B
are similar matrices where
A
A
A
is a scalar matrix, then
A
=
B
A=B
A
=
B
.
Save
Check
Details
