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Question 44 - Week 6 Practice | Prasnya
Q44
00:00
2 Apr 2023
Q44.
Consider the vector space
V
=
{
[
a
b
a
b
]
:
a
,
b
∈
R
}
V=\left\{\begin{bmatrix}a&b\\a&b\end{bmatrix}:a,b\in\mathbb{R}\right\}
V
=
{
[
a
a
b
b
]
:
a
,
b
∈
R
}
and
T
:
R
3
→
V
T:\mathbb{R}^3\to V
T
:
R
3
→
V
defined by
T
(
x
,
y
,
z
)
=
[
x
+
y
x
+
y
+
z
x
+
y
x
+
y
+
z
]
T(x,y,z)=\begin{bmatrix}x+y&x+y+z\\x+y&x+y+z\end{bmatrix}
T
(
x
,
y
,
z
)
=
[
x
+
y
x
+
y
x
+
y
+
z
x
+
y
+
z
]
. Choose the correct option.
A
T
T
T
is onto but not one-one.
B
T
T
T
is one-one but not onto.
C
T
T
T
is both one-one and onto.
D
T
T
T
is neither one-one nor onto.
Save
Check
Details
Q44
00:00
2 Apr 2023
Q44.
Consider the vector space
V
=
{
[
a
b
a
b
]
:
a
,
b
∈
R
}
V=\left\{\begin{bmatrix}a&b\\a&b\end{bmatrix}:a,b\in\mathbb{R}\right\}
V
=
{
[
a
a
b
b
]
:
a
,
b
∈
R
}
and
T
:
R
3
→
V
T:\mathbb{R}^3\to V
T
:
R
3
→
V
defined by
T
(
x
,
y
,
z
)
=
[
x
+
y
x
+
y
+
z
x
+
y
x
+
y
+
z
]
T(x,y,z)=\begin{bmatrix}x+y&x+y+z\\x+y&x+y+z\end{bmatrix}
T
(
x
,
y
,
z
)
=
[
x
+
y
x
+
y
x
+
y
+
z
x
+
y
+
z
]
. Choose the correct option.
A
T
T
T
is onto but not one-one.
B
T
T
T
is one-one but not onto.
C
T
T
T
is both one-one and onto.
D
T
T
T
is neither one-one nor onto.
Save
Check
Details
