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Question 12 - Week 7 Practice | Prasnya
Q12
00:00
16 Mar 2025
Q12.
Let
A
=
[
2
−
3
4
1
]
A=\begin{bmatrix}2&-3\\4&1\end{bmatrix}
A
=
[
2
4
−
3
1
]
. Choose all the correct options.
A
If
A
A
A
is equivalent to a matrix
B
B
B
, then they have the same rank, trace, and determinant.
B
B
∈
M
2
×
2
(
R
)
B\in M_{2\times2}(\mathbb{R})
B
∈
M
2
×
2
(
R
)
is a matrix with the same rank, trace, and determinant as
A
A
A
. Then
A
A
A
and
B
B
B
are similar.
C
B
∈
M
2
×
2
(
R
)
B\in M_{2\times2}(\mathbb{R})
B
∈
M
2
×
2
(
R
)
is a matrix such that
A
=
[
0
−
1
5
0
]
B
A=\begin{bmatrix}0&-1\\5&0\end{bmatrix}B
A
=
[
0
5
−
1
0
]
B
. Then
A
A
A
and
B
B
B
are equivalent.
D
A
A
A
is equivalent to any
2
×
2
2\times2
2
×
2
orthogonal matrix.
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Check
Details
Q12
00:00
16 Mar 2025
Q12.
Let
A
=
[
2
−
3
4
1
]
A=\begin{bmatrix}2&-3\\4&1\end{bmatrix}
A
=
[
2
4
−
3
1
]
. Choose all the correct options.
A
If
A
A
A
is equivalent to a matrix
B
B
B
, then they have the same rank, trace, and determinant.
B
B
∈
M
2
×
2
(
R
)
B\in M_{2\times2}(\mathbb{R})
B
∈
M
2
×
2
(
R
)
is a matrix with the same rank, trace, and determinant as
A
A
A
. Then
A
A
A
and
B
B
B
are similar.
C
B
∈
M
2
×
2
(
R
)
B\in M_{2\times2}(\mathbb{R})
B
∈
M
2
×
2
(
R
)
is a matrix such that
A
=
[
0
−
1
5
0
]
B
A=\begin{bmatrix}0&-1\\5&0\end{bmatrix}B
A
=
[
0
5
−
1
0
]
B
. Then
A
A
A
and
B
B
B
are equivalent.
D
A
A
A
is equivalent to any
2
×
2
2\times2
2
×
2
orthogonal matrix.
Save
Check
Details
