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Question 29 - Week 8 Practice | Prasnya
Q29
00:00
3 Dec 2023
Q29.
Let
A
A
A
be an
n
×
n
n\times n
n
×
n
orthogonal matrix. Which statements are true?
A
The rows of
A
A
A
form an orthonormal basis for
R
n
\mathbb{R}^n
R
n
.
B
Suppose
T
T
T
is the linear transformation corresponding to
A
A
A
, then
∥
T
v
∥
=
∥
v
∥
\lVert Tv\rVert=\lVert v\rVert
∥
T
v
∥
=
∥
v
∥
for any
v
∈
R
n
v\in\mathbb{R}^n
v
∈
R
n
.
C
The system
A
x
=
b
Ax=b
A
x
=
b
has a unique solution for every
b
∈
R
n
b\in\mathbb{R}^n
b
∈
R
n
.
D
The rows of
A
A
A
form an orthogonal basis but not an orthonormal basis for
R
n
\mathbb{R}^n
R
n
.
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Details
Q29
00:00
3 Dec 2023
Q29.
Let
A
A
A
be an
n
×
n
n\times n
n
×
n
orthogonal matrix. Which statements are true?
A
The rows of
A
A
A
form an orthonormal basis for
R
n
\mathbb{R}^n
R
n
.
B
Suppose
T
T
T
is the linear transformation corresponding to
A
A
A
, then
∥
T
v
∥
=
∥
v
∥
\lVert Tv\rVert=\lVert v\rVert
∥
T
v
∥
=
∥
v
∥
for any
v
∈
R
n
v\in\mathbb{R}^n
v
∈
R
n
.
C
The system
A
x
=
b
Ax=b
A
x
=
b
has a unique solution for every
b
∈
R
n
b\in\mathbb{R}^n
b
∈
R
n
.
D
The rows of
A
A
A
form an orthogonal basis but not an orthonormal basis for
R
n
\mathbb{R}^n
R
n
.
Save
Check
Details
