Question 25 - Week 4 Practice | Prasnya
Prasnya
Continue with Google
Practice path
Dashboard
Exam
Qualifier / Quiz 1
Go to subject
Mathematics 2
Go to chapter
Week 4
Question 25
00:00
Est. 1 min
Marks:
+1.00
0.00
Passage
Choose the correct basis for each of the given vector spaces in the subquestions. Consider the following sets:
B
1
=
{
[
3
−
3
0
0
]
,
[
0
0
−
5
5
]
}
B_1=\left\{\begin{bmatrix}3&-3\\0&0\end{bmatrix},\begin{bmatrix}0&0\\-5&5\end{bmatrix}\right\}
,
B
2
=
{
[
0
2
−
2
0
]
}
B_2=\left\{\begin{bmatrix}0&2\\-2&0\end{bmatrix}\right\}
, and
B
3
=
{
[
1
0
0
−
1
]
,
[
0
−
2
0
0
]
,
[
0
0
3
0
]
}
B_3=\left\{\begin{bmatrix}1&0\\0&-1\end{bmatrix},\begin{bmatrix}0&-2\\0&0\end{bmatrix},\begin{bmatrix}0&0\\3&0\end{bmatrix}\right\}
.
Question
W
1
=
{
A
∈
M
2
×
2
(
R
)
:
A
T
=
−
A
}
W_1=\{A\in M_{2\times2}(\mathbb{R}):A^T=-A\}
.
Comprehension
Easy Difficulty
27 October 2024
A
B
1
B_1
B
B
2
B_2
C
B
3
B_3
