Linear Algebra_Simple Quiz

Choose the correct one: A finite set which spans the Vector Space V. Then V is?

• Linearly Independent

• Linearly dependent

• Finite Dimensional

• Finite Subspace

Which one is correct: A set which is not linearly independent, then it is ?

• Linearly Dependent

• Basis

• Span

• Minimal generating set

Subset of Linearly dependent set is linearly dependent

• True
• False

Which of the following is not a basis for R x R x R over R:

• S={(1,0,0), (0,1,0), (1,0,1)}

• S={(1,0,0), (0,1,0), (0,0,1)}

• S={(1,0,0), (1,1,0), (1,1,1)}

• S={(1,0,0), (1,1,0)}

Which of the following is not a trivial subspace of V over F

• {0} 

• V 

• {(1,0,0), (0,1,0), (0,0,1)}

Intersection of Subspaces of a Vector Space is again a Subspace of that Vector Space

• True
• False

R is a Vector Space over C

• True
• False

Super set of Linearly independent is linearly independent

• True
• False

Any two bases of a finite dimensional vector space V have the different number of elements

• True
• False

Dimension of M_2(R)?

• 3

• 2

• 14

• 4