Question -1

Consider the vector space of all 10x10 diagonal matrices. The dimension of this vector space is 20.

select one:

a. True

b. False

Question -2

If a vector space does not have a finite basis then the vector space is infinite dimensional.

select one:

a. True

b. False

Question -3

A subset S={u} of a vector space V is linearly independent if u 0

select one:

a. True

b. False

Question -4

A basis of a vector space is the smallest set that spans the vector space.

select one:

a. True

b. False

Question -5

The set {t, 1-t, 1+t-t} is basis for P2.

Select one:

a. True

b. False

Question -6

Suppose if T is a linearly independent subset of a vector space V, then T is a basis for span(T)

Select one:

a. True

b. False

Question -7

Let A be a 6x6 non-singular matrix. Then the rows of A span the vector space R.

Select one:

a. True

b. False

Question -8

The set { (1,2,3) ,(2,3,1) ,(-1,2.-3) } forms a basis for the vector space R

Select one:

a. True

b. False

Question -9

W is a subspace of the vector space V such that dim(W) =dim(V).Then W V

Select one:

a. True

b. False

Question -10

A basis of a vector space is the smallest linearly independent subset of that vector space.

Select one:

a. True

b. False

Question -11

The set {(1,0,0),(1,1,0)} spans the vector space R.

Select one:

a. True

b. False

Question -12

The union of two subspaces of a vector space is a subspace.

Select one:

a. True

b. False

Question -13

Consider the vector space of real numbers. Then every subset of it with only one vector(the vector being non-zero)forms a basis for the vector space.

Select one:

a. True

b. False

Question -14

The set { (1,1,1,1), (0,0,0,0) ,(-1,-1,-1,-1)}.spans the vector space R4.

Select one:

a. True

b. False

Question -15

Every subspace of a finite dimensional vector space is finite dimensional.

Select one:

a. True

b. False

Question -16

The set { (2,-3,1),(-8,12,-4)} is a linearly independent subset of R.

Select one:

a. True

b. False

Question -17

Let A be a non-singular 4x4 matrix. Then the rows of A form a basis for R4.

Select one:

a. True

b. False

Question -18

The row space of a 4x5 matrix is a subspace of R4

Select one:

a. True

b. False

Question -19

The set {1,x+1,x+x+1}spans P2.

Select one:

a. True

b. False

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