Linear Algebra: UNIT I: Vector Spaces
Vector Spaces: Multiple Choice Questions and Answers
Linear Algebra
Multiple Choice Questions and Answers - Linear Algebra: UNIT I: Vector Spaces
Linear Algebra
UNIT I: VECTOR SPACES
Multiple
Choice Questions and Answers
1. In any vector space
V, the two subspaces are
(A)
{0,0}
(B)
{F, V}
(C)
{ 1, 1 }
(D) { 0,
V}
2. How many matrices
are there in the vector space Mm×n(z2).
(A)
mn
(B)
mn
(C)
nm
(D) 2mn
3. If x, y and z are
vectors in a vector space V such that x+z = y + z then
(A) x=y
(B)
x=x
(C)
y=y
(D)
x=z
4. The union of any two
subspaces of a vector space is
(A)
Subspace
(B)
Not subspace
(C)
Field
(D)
Not field
5. A subset W of a
vector space V is a subspace of V if and only if
(A)
Span (S) = 0
(B) L(W)
= W
(C)
Gen (W) = 0
(D)
W+V=0
6. Let V be a vector
space over F and S1 
S2 V then
(A)
S2 S1
(B)
Span (S1) ≠ Span (S2)
(C) L(S1) L(S2)
(D)
S1 ≠ S2
7. Let V be a vector
space over F and S1 V1, S2 V
then
(A) L(S1∪S2)=L(S1)+L(S2)
(B)
L(S1∩S2)=S1∩S2
(C)
L(S1)+L(S)
(D)
L(S1S2)=L(S1S2 ‒ S2S1)
8. The vectors v1
= (1, 2, 3), V2 = (5, 6, ‒1) and v3 = (3, 2, 1) form a
(A)
Linearly dependent set
(B)
Linearly independent set
(C)
Vector space
(D)
Field
9. The vector space Pn(F)
has dimensions
(A)
n
(B) n+1
(C)
n+2
(D)
n+3
10. Let W1
and W2 be the subspaces of a finite dimensional vector space V. The
necessary and sufficient conditions on W1 and W2 is
(A) dim
(W1 ∩ W2) = dim (W1)
(B)
dim (W1 W2) = dim (W1)
(C)
dim (W1 ∪ W2)
= dim (W1 – W2)
(D)
dim (W1) ≤ dim (W2)
Linear Algebra: UNIT I: Vector Spaces : Tag: maths, mathematics : Linear Algebra - Vector Spaces: Multiple Choice Questions and Answers
Linear Algebra: UNIT I: Vector Spaces
Under Subject
Linear Algebra
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