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Week 5 Practice Questions | Prasnya
Q1
00:00
3 Aug 2025
Q1.
Let
A
A
A
be a
3
×
5
3\times 5
3
×
5
matrix whose row echelon form is
[
1
2
−
1
2
1
0
0
1
3
−
2
0
0
0
k
0
]
,
\begin{bmatrix}1&2&-1&2&1\\0&0&1&3&-2\\0&0&0&k&0\end{bmatrix},
1
0
0
2
0
0
−
1
1
0
2
3
k
1
−
2
0
,
where
k
∈
R
k\in\mathbb{R}
k
∈
R
. Choose the correct option.
A
The nullity of
A
A
A
is independent of the value of
k
k
k
.
B
The nullity of
A
A
A
depends on
k
k
k
, and the set of all possible values for the nullity is
{
2
}
\{2\}
{
2
}
.
C
The nullity of
A
A
A
depends on
k
k
k
, and the set of all possible values for the nullity is
{
0
,
1
,
2
,
3
,
4
,
5
}
\{0,1,2,3,4,5\}
{
0
,
1
,
2
,
3
,
4
,
5
}
.
D
The nullity of
A
A
A
depends on
k
k
k
, and the set of all possible values for the nullity is
{
2
,
3
}
\{2,3\}
{
2
,
3
}
.
Save
Check
Details
Q1
00:00
3 Aug 2025
Q1.
Let
A
A
A
be a
3
×
5
3\times 5
3
×
5
matrix whose row echelon form is
[
1
2
−
1
2
1
0
0
1
3
−
2
0
0
0
k
0
]
,
\begin{bmatrix}1&2&-1&2&1\\0&0&1&3&-2\\0&0&0&k&0\end{bmatrix},
1
0
0
2
0
0
−
1
1
0
2
3
k
1
−
2
0
,
where
k
∈
R
k\in\mathbb{R}
k
∈
R
. Choose the correct option.
A
The nullity of
A
A
A
is independent of the value of
k
k
k
.
B
The nullity of
A
A
A
depends on
k
k
k
, and the set of all possible values for the nullity is
{
2
}
\{2\}
{
2
}
.
C
The nullity of
A
A
A
depends on
k
k
k
, and the set of all possible values for the nullity is
{
0
,
1
,
2
,
3
,
4
,
5
}
\{0,1,2,3,4,5\}
{
0
,
1
,
2
,
3
,
4
,
5
}
.
D
The nullity of
A
A
A
depends on
k
k
k
, and the set of all possible values for the nullity is
{
2
,
3
}
\{2,3\}
{
2
,
3
}
.
Save
Check
Details
