Learning Outcomes

After completing this chapter, students should be able to do the following.

  • Determine whether sets are closed under addition and/or scalar multiplication.
  • Determine whether a set of vectors is a basis of a subspace or .
  • Write the coordinates of a vector with respect to a given basis of .
  • Identify the dimension of the span of a given set of vectors.
  • Find a basis for each of the following: the row space, the column space, and the null space of a given matrix.
  • Prove elementary theorems concerning rank of a matrix and the relationship between rank and nullity.