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Question 28 - Week 8 Practice | Prasnya
Q28
00:00
24 Mar 2024
Q28.
Choose the correct options from the following.
A
If
A
A
A
and
B
B
B
are orthogonal matrices, then
A
B
AB
A
B
is also orthogonal.
B
If
A
A
A
is orthogonal, then
A
−
1
A^{-1}
A
−
1
is also an orthogonal matrix.
C
Let
A
A
A
be an
n
×
n
n\times n
n
×
n
orthogonal matrix. Let
R
R
R
be the set of rows of
A
A
A
and
C
C
C
be the set of columns of
A
A
A
. Then exactly one of
R
R
R
or
C
C
C
is an orthogonal subset of vectors.
D
If
A
A
A
is an
n
×
n
n\times n
n
×
n
orthogonal matrix, then
∥
A
x
∥
=
∥
x
∥
\lVert Ax\rVert=\lVert x\rVert
∥
A
x
∥
=
∥
x
∥
for any
x
∈
R
n
x\in\mathbb{R}^n
x
∈
R
n
.
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Details
Q28
00:00
24 Mar 2024
Q28.
Choose the correct options from the following.
A
If
A
A
A
and
B
B
B
are orthogonal matrices, then
A
B
AB
A
B
is also orthogonal.
B
If
A
A
A
is orthogonal, then
A
−
1
A^{-1}
A
−
1
is also an orthogonal matrix.
C
Let
A
A
A
be an
n
×
n
n\times n
n
×
n
orthogonal matrix. Let
R
R
R
be the set of rows of
A
A
A
and
C
C
C
be the set of columns of
A
A
A
. Then exactly one of
R
R
R
or
C
C
C
is an orthogonal subset of vectors.
D
If
A
A
A
is an
n
×
n
n\times n
n
×
n
orthogonal matrix, then
∥
A
x
∥
=
∥
x
∥
\lVert Ax\rVert=\lVert x\rVert
∥
A
x
∥
=
∥
x
∥
for any
x
∈
R
n
x\in\mathbb{R}^n
x
∈
R
n
.
Save
Check
Details
