# Math 210-01: Linear Algebra: Reading Homework 4.6

1. Matrix Rank and Systems : with what is this section concerned?
1. Row and Column Spaces : what are the row and column space of a matrix?
1. row spaces : what do we know about the row spaces of row-equivalent matrices? how are the rows of these related to the spaces?
2. finding row spaces and bases : how can we find the row space of a matrix? how can we find a basis for the subspace of Rn spanned by a set of vectors?
3. column spaces : how can we find a basis for the column space of a matrix?
4. dimension : how are the dimension of the row and column spaces of a matrix related?
2. Rank : what is the rank of a matrix? how can we find the rank of a matrix?
3. Nullspace : what is the nullspace of a matrix? how is it related to the nullity of the matrix? how is it a solution space?
1. rank, nullity, size : how are the dimensions of a matrix related to its nullity and rank?
4. Nonhomogeneous Systems : how are solutions to a nonhomogeneous system related to the nullspace of a the coefficient matrix?
1. column space : how is the column space of a coefficient matrix related to solutions of a nonhomogeneous system?
5. Square Systems : what conditions are equivalent when we discuss ``square'' linear equations?

Math 210-01: Linear Algebra: Reading Homework 4.6