LINEAR ALGEBRA UNIT 2 EXAM (T/F)
QUESTIONS WITH COMPLETE
ANSWERS
Two vectors in R^n are equal if and only if their corresponding components are equal -
Answer-True
The vector -V is the additive identity of V - Answer-False
To subtract two vectors in R^n, subtract their corresponding components - Answer-True
The zero vector 0 in R^n is the additive inverse of a vector - Answer-False
To show that a set is not a vector space, it is sufficient to show that just one axiom is not
satisfied - Answer-True
The set of all first-degree polynomials with the standard operations is a vector space -
Answer-False
The set of all pairs of real numbers of the form (0,y,) with the standard operations on
R^2, is a vector space - Answer-True
Every vector space V contains two proper subspace that are the zero subspace and
itself - Answer-True
If W is a subspace of R^2, then W must contain the vector (0,0) - Answer-True
If W is a subspace of a vector space V, then it has closure under addition as defined in
V - Answer-True
If W is the subspace of a vector space V, then W is also a vector space - Answer-True
A set S ={V1, V2, ..., Vk}, k>2 is linearly dependent if and only if at least one of the
vectors Vi can be written as a linear combination of the other vectors in S - Answer-false
If the subset S spans a vector space V, then every vector in V can be written as a linear
combination of the vectors in S - Answer-True
If dim(V) = n, then any set of n+1 vectors in V must be linearly dependent - Answer-True
If dim(V) = n, then any set of n-1 vectors in V must be linearly independent - Answer-
False
QUESTIONS WITH COMPLETE
ANSWERS
Two vectors in R^n are equal if and only if their corresponding components are equal -
Answer-True
The vector -V is the additive identity of V - Answer-False
To subtract two vectors in R^n, subtract their corresponding components - Answer-True
The zero vector 0 in R^n is the additive inverse of a vector - Answer-False
To show that a set is not a vector space, it is sufficient to show that just one axiom is not
satisfied - Answer-True
The set of all first-degree polynomials with the standard operations is a vector space -
Answer-False
The set of all pairs of real numbers of the form (0,y,) with the standard operations on
R^2, is a vector space - Answer-True
Every vector space V contains two proper subspace that are the zero subspace and
itself - Answer-True
If W is a subspace of R^2, then W must contain the vector (0,0) - Answer-True
If W is a subspace of a vector space V, then it has closure under addition as defined in
V - Answer-True
If W is the subspace of a vector space V, then W is also a vector space - Answer-True
A set S ={V1, V2, ..., Vk}, k>2 is linearly dependent if and only if at least one of the
vectors Vi can be written as a linear combination of the other vectors in S - Answer-false
If the subset S spans a vector space V, then every vector in V can be written as a linear
combination of the vectors in S - Answer-True
If dim(V) = n, then any set of n+1 vectors in V must be linearly dependent - Answer-True
If dim(V) = n, then any set of n-1 vectors in V must be linearly independent - Answer-
False
