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Question 18 - Week 5 Practice | Prasnya
Q18
00:00
20 Nov 2022
Q18.
Which of the following options are true?
A
If
A
A
A
is a non-zero matrix of order
4
×
3
4\times3
4
×
3
and
rank
(
A
)
=
3
\operatorname{rank}(A)=3
rank
(
A
)
=
3
, then the rows of
A
A
A
are linearly independent.
B
If
A
A
A
is a non-zero matrix of order
4
×
3
4\times3
4
×
3
and
rank
(
A
)
=
3
\operatorname{rank}(A)=3
rank
(
A
)
=
3
, then the columns of
A
A
A
are linearly independent.
C
If
A
A
A
is a non-zero matrix of order
m
×
(
m
+
1
)
m\times(m+1)
m
×
(
m
+
1
)
,
m
>
1
m>1
m
>
1
, then the maximum possible nullity of
A
A
A
is
m
m
m
.
D
If
A
A
A
is a non-zero matrix of order
4
×
5
4\times5
4
×
5
and
rank
(
A
)
=
3
\operatorname{rank}(A)=3
rank
(
A
)
=
3
, then the dimension of the solution space of
A
x
=
0
Ax=0
A
x
=
0
is
2
2
2
.
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Check
Details
Q18
00:00
20 Nov 2022
Q18.
Which of the following options are true?
A
If
A
A
A
is a non-zero matrix of order
4
×
3
4\times3
4
×
3
and
rank
(
A
)
=
3
\operatorname{rank}(A)=3
rank
(
A
)
=
3
, then the rows of
A
A
A
are linearly independent.
B
If
A
A
A
is a non-zero matrix of order
4
×
3
4\times3
4
×
3
and
rank
(
A
)
=
3
\operatorname{rank}(A)=3
rank
(
A
)
=
3
, then the columns of
A
A
A
are linearly independent.
C
If
A
A
A
is a non-zero matrix of order
m
×
(
m
+
1
)
m\times(m+1)
m
×
(
m
+
1
)
,
m
>
1
m>1
m
>
1
, then the maximum possible nullity of
A
A
A
is
m
m
m
.
D
If
A
A
A
is a non-zero matrix of order
4
×
5
4\times5
4
×
5
and
rank
(
A
)
=
3
\operatorname{rank}(A)=3
rank
(
A
)
=
3
, then the dimension of the solution space of
A
x
=
0
Ax=0
A
x
=
0
is
2
2
2
.
Save
Check
Details
