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Question 17 - Week 6 Practice | Prasnya
Q17
00:00
1 Dec 2024
Q17.
Let
T
:
R
n
→
R
m
T:\mathbb{R}^n\to\mathbb{R}^m
T
:
R
n
→
R
m
be a linear transformation. Choose the correct option that guarantees that
T
T
T
is bijective.
A
m
=
n
m=n
m
=
n
.
B
T
T
T
maps a basis of
R
m
\mathbb{R}^m
R
m
to a basis of
R
n
\mathbb{R}^n
R
n
.
C
The matrix representation of
T
T
T
with respect to any ordered basis is square and invertible.
D
rank
(
T
)
=
m
\operatorname{rank}(T)=m
rank
(
T
)
=
m
.
Save
Check
Details
Q17
00:00
1 Dec 2024
Q17.
Let
T
:
R
n
→
R
m
T:\mathbb{R}^n\to\mathbb{R}^m
T
:
R
n
→
R
m
be a linear transformation. Choose the correct option that guarantees that
T
T
T
is bijective.
A
m
=
n
m=n
m
=
n
.
B
T
T
T
maps a basis of
R
m
\mathbb{R}^m
R
m
to a basis of
R
n
\mathbb{R}^n
R
n
.
C
The matrix representation of
T
T
T
with respect to any ordered basis is square and invertible.
D
rank
(
T
)
=
m
\operatorname{rank}(T)=m
rank
(
T
)
=
m
.
Save
Check
Details
