LINEAR ALGEBRA FINAL EXAM QUESTIONS AND ANSWERS

LINEAR ALGEBRA FINAL EXAM
QUESTIONS AND ANSWERS
Suppose a vector space V contains n linearly independent vectors. Which of the
following statements is always true?
a. The dimension of V is n
b. The n linearly independent vectors span V.
c. V contains a subspace of dimension n.
d. V is finite dimensional - Answer-c

Suppose a vector space V is spanned by n vectors. Which of the following statements is
always true?
a. The dimension of V is greater than n.
b. The dimension of V is less than n.
c. V contains a subspace of dimension n.
d. V is finite dimensional. - Answer-d

Suppose a vector space V contains a subspace of dimension n. Which of the following
statements is always true?
a. The dimension of V is greater than n.
b. The dimension of V is less than n.
c. V contains a set of n linearly independent vectors.
d. v is finite dimensional. - Answer-c

Suppose an mxn matrix A has a pivot position in every row. Which of the following
statements is always true?
a. The nullity of A is equal to n.
b. The nullity of A is equal to m.
c. The rank of A is equal to n.
d. the rank of A is equal to m. - Answer-d

Suppose an mxn matrix A has rank equal to p which of the following statements is
always true?
a. The nullity of A is equal to n-p.
b. The nullity of A is equal to m-p.
c. The nullity of A is equal to n.
d. The nullity of A is equal to m. - Answer-a

Suppose an mxn matrix A has rank equal to p. Which of the following statements is
always true?
a. The dimension of the column space of A is equal to n-p.
b. The dimension of the null space of A is equal to m-p.
c. The dimension of the column space of A is equal to p.
d. The dimension of the null space of A is equal to p. - Answer-c