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Question 34 - Week 7 Practice | Prasnya
Q34
00:00
20 Nov 2022
Q34.
Which of the following options are true?
A
Every matrix is similar to itself.
B
If
A
A
A
is similar to
B
B
B
, then
A
−
1
A^{-1}
A
−
1
is similar to
B
−
1
B^{-1}
B
−
1
.
C
[
2
1
0
2
]
\begin{bmatrix}2&1\\0&2\end{bmatrix}
[
2
0
1
2
]
is similar to
[
2
0
0
2
]
\begin{bmatrix}2&0\\0&2\end{bmatrix}
[
2
0
0
2
]
.
D
If
A
A
A
is similar to
B
+
C
B+C
B
+
C
, then
rank
(
A
)
=
rank
(
B
)
+
rank
(
C
)
\operatorname{rank}(A)=\operatorname{rank}(B)+\operatorname{rank}(C)
rank
(
A
)
=
rank
(
B
)
+
rank
(
C
)
.
Save
Check
Details
Q34
00:00
20 Nov 2022
Q34.
Which of the following options are true?
A
Every matrix is similar to itself.
B
If
A
A
A
is similar to
B
B
B
, then
A
−
1
A^{-1}
A
−
1
is similar to
B
−
1
B^{-1}
B
−
1
.
C
[
2
1
0
2
]
\begin{bmatrix}2&1\\0&2\end{bmatrix}
[
2
0
1
2
]
is similar to
[
2
0
0
2
]
\begin{bmatrix}2&0\\0&2\end{bmatrix}
[
2
0
0
2
]
.
D
If
A
A
A
is similar to
B
+
C
B+C
B
+
C
, then
rank
(
A
)
=
rank
(
B
)
+
rank
(
C
)
\operatorname{rank}(A)=\operatorname{rank}(B)+\operatorname{rank}(C)
rank
(
A
)
=
rank
(
B
)
+
rank
(
C
)
.
Save
Check
Details
