#Q4 Let V be a vector Space of all 3×3 matrix and W Consist of all 3×3 matrices with zero determinant
Anonymous Quiz
16%
W is not a subspace of v.
43%
W May or may not be subspace of v
25%
W is not a subspace of v
16%
None of these
#Q5 Which of the following are true?
Anonymous Quiz
56%
Any field forms a vectors space over itself
8%
Any field does not Forms a vector space over itself
21%
Any field, R is vector space over C
16%
All of the above
#Q6 The necessary and sufficient condition for a nonempty subset W of a vector space V(F) to be a subspace is/are-
Anonymous Quiz
18%
u+v ∈ W and au ∈ W ∀ u, v ∈ W and a ∈ F
15%
au+v ∈ W ∀ u, v ∈ W and a ∈ F
25%
au+bv ∈ W for all u,v ∈W and a,b ∈ F
43%
All of the above
#Q7 Let V be real Vector space of all mapping from R to R { f ∈V | f( -x)=f( x)}(b) { f ∈V |f (-x)=-f( x) } then
Anonymous Quiz
52%
Both A and B are Subspace
15%
Neither A nor B is subspace
25%
A is subspace but not B
8%
A is not Subspace But B is
#Q8 Let V=R³ and w= {x,y,z ∈ V|4x-2y+z=0} then which of the following is not true
Anonymous Quiz
21%
W is subspace of V
16%
α, β ∈ W ⇒ α+β ∈ W
59%
W is not a subspace of V
5%
α, β ∈ W ⇒ α-β ∈ W
#Q9 If S1 and S2 are subspaces of linear space L then
Anonymous Quiz
19%
S1+[S]2 is a Subspace of L
24%
S1-[ S]2 is a Subspace of L
51%
Both (a) & (b) are true
7%
Neither (a) Nor (b) is true
#Q10 V be vector space of all 2×2 matrices over R and S be the set of idempotent matrices then.
Anonymous Quiz
19%
S is not Subspace of V as vector addition is not closed
28%
S is not subspace as Scaler multiplication is not closed
41%
Both (a) & (b)
13%
None of these
𝐓𝐡𝐞𝐲 𝐰𝐞𝐫𝐞 𝐨𝐧𝐜𝐞 𝐢𝐧 𝐲𝐨𝐮𝐫 𝐞𝐱𝐚𝐜𝐭 𝐩𝐨𝐬𝐢𝐭𝐢𝐨𝐧. 𝐓𝐡𝐞𝐲 𝐚𝐜𝐜𝐞𝐩𝐭𝐞𝐝 𝐭𝐡𝐞 𝐜𝐡𝐚𝐥𝐥𝐞𝐧𝐠𝐞. 𝐓𝐡𝐞𝐲 𝐬𝐮𝐜𝐜𝐞𝐞𝐝𝐞𝐝. 𝐓𝐡𝐞 𝐨𝐧𝐥𝐲 𝐪𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐢𝐬: 𝐖𝐢𝐥𝐥 𝐲𝐨𝐮?
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
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𝐓𝐡𝐞𝐲 𝐰𝐞𝐫𝐞 𝐨𝐧𝐜𝐞 𝐢𝐧 𝐲𝐨𝐮𝐫 𝐞𝐱𝐚𝐜𝐭 𝐩𝐨𝐬𝐢𝐭𝐢𝐨𝐧. 𝐓𝐡𝐞𝐲 𝐚𝐜𝐜𝐞𝐩𝐭𝐞𝐝 𝐭𝐡𝐞 𝐜𝐡𝐚𝐥𝐥𝐞𝐧𝐠𝐞. 𝐓𝐡𝐞𝐲 𝐬𝐮𝐜𝐜𝐞𝐞𝐝𝐞𝐝. 𝐓𝐡𝐞 𝐨𝐧𝐥𝐲 𝐪𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐢𝐬: 𝐖𝐢𝐥𝐥 𝐲𝐨𝐮?
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
#Q1 Let F be countably infinite field, V is non – finitely generated vector space and S is also countably infinite L(S)=V, then
Anonymous Quiz
36%
V is uncountable
21%
|V|=|P(R)|
28%
|V|=|Z|
16%
|V|=|P(N)|
#Q2 Which of the following statements is/are true?
Anonymous Quiz
16%
A finitely generated vector space vector space V over a finite field can be expressed as infinite
32%
A vector space V can be expressed as finite union of proper subspace of V on an infinite field
47%
A vector space V can not be expressed as finite union of proper subspace of V over an infinite field
5%
None of these
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#Q3 Which of the following statements is/are true.
Anonymous Quiz
8%
Any set containing zero vector can be linearly independent
21%
Super set of linearly independent set is linearly independent
56%
Super set of linearly dependent set is linearly dependent
16%
Subset of a linearly independent set need not to be linearly independent
#Q4 Which of the following statement is/are true?
Anonymous Quiz
40%
Every singleton set of a vector is linearly independent
25%
Empty set is vector is linearly independent set
21%
Every non - empty set of non - zero vectors has non – empty linearly dependent subset
14%
S ; any set is linearly dependent if it S every subset is linearly dependent
#Q5 Let V be a vector space. Then which of the following is/are true?
Anonymous Quiz
30%
If V vector space of continuous functions, then any subset of V is linearly independent if Wronskian
35%
Any two distinct vectors U and W of any vector space V are always linearly independent
23%
Let S1⊆ S2 ⊆V and S2 is linearly dependent then S1 is also linearly dependent
12%
None of these
#Q6 Let V be a zero space {0} of dimension {0}, then V
Anonymous Quiz
8%
Cannot be generated
51%
Generated by {0}
41%
Generated by ϕ
0%
None of these
#Q7 Let A be a m×n matrix. Suppose that rank (A) = n then
Anonymous Quiz
18%
The rows of A from a linearly independent set
45%
The columns of A from a linearly independent set
10%
The columns of A do not form a linearly independent set
27%
A is non-singular
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#Q8 Which of the following statement is/are true?
Anonymous Quiz
11%
Solution of nth order homogenous differential equation does not form a vector space
32%
Solution of nth order non- homogenous differential equation form a vector space
54%
Solution of nth order homogenous differential equation form a vector space
3%
None of them form a vector space
#Q9 Which of the following statements is given by Invariance theorem.
Anonymous Quiz
23%
Basis is the minimal spanning set and maximal independent set in the sense of cardinality
38%
Every Finitely generated vector space has a basis
32%
If B1 and B2 are two bases of any finitely generated vector space, then |B1 |=|B2 |
8%
dim V= Basis of V
#Q10 Which of the following is/are finitely generated vector space?
Anonymous Quiz
13%
R(Q)
16%
C(Q)
55%
Q(√2)(Q)
15%
Q(Q(√2)
𝐓𝐡𝐞𝐲 𝐰𝐞𝐫𝐞 𝐨𝐧𝐜𝐞 𝐢𝐧 𝐲𝐨𝐮𝐫 𝐞𝐱𝐚𝐜𝐭 𝐩𝐨𝐬𝐢𝐭𝐢𝐨𝐧. 𝐓𝐡𝐞𝐲 𝐚𝐜𝐜𝐞𝐩𝐭𝐞𝐝 𝐭𝐡𝐞 𝐜𝐡𝐚𝐥𝐥𝐞𝐧𝐠𝐞. 𝐓𝐡𝐞𝐲 𝐬𝐮𝐜𝐜𝐞𝐞𝐝𝐞𝐝. 𝐓𝐡𝐞 𝐨𝐧𝐥𝐲 𝐪𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐢𝐬: 𝐖𝐢𝐥𝐥 𝐲𝐨𝐮?
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
𝐄𝐧𝐫𝐨𝐥𝐥 𝐍𝐨𝐰 :- https://bit.ly/49PVrCW
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