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Question 1 - Week 6 Practice | Prasnya
Q1
00:00
6 Apr 2026
Q1.
Let
T
:
R
3
→
R
3
T:\mathbb{R}^3\to\mathbb{R}^3
T
:
R
3
→
R
3
be a linear transformation such that
T
2
=
T
T^2=T
T
2
=
T
, and
rank
(
T
)
=
2
\operatorname{rank}(T)=2
rank
(
T
)
=
2
. Which of the following statements is correct?
A
T
T
T
is the identity transformation.
B
T
T
T
maps every vector in
R
3
\mathbb{R}^3
R
3
to a vector with at least one zero component.
C
T
T
T
is not injective.
D
Im
(
T
)
=
R
3
\operatorname{Im}(T)=\mathbb{R}^3
Im
(
T
)
=
R
3
.
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Check
Details
Q1
00:00
6 Apr 2026
Q1.
Let
T
:
R
3
→
R
3
T:\mathbb{R}^3\to\mathbb{R}^3
T
:
R
3
→
R
3
be a linear transformation such that
T
2
=
T
T^2=T
T
2
=
T
, and
rank
(
T
)
=
2
\operatorname{rank}(T)=2
rank
(
T
)
=
2
. Which of the following statements is correct?
A
T
T
T
is the identity transformation.
B
T
T
T
maps every vector in
R
3
\mathbb{R}^3
R
3
to a vector with at least one zero component.
C
T
T
T
is not injective.
D
Im
(
T
)
=
R
3
\operatorname{Im}(T)=\mathbb{R}^3
Im
(
T
)
=
R
3
.
Save
Check
Details
