Standards: Chapter 2

I understand addition and scalar multiplication of vectors
algebraically and geometrically. I know the algebraic properties that
vector addition and scalar multiplication satisfy. I know how to
multiply an nxm matrix A by a vector x in R^m

I can state the definition of the span of a set of vectors. I can
determine if a vector in R^n is in the span of a set of vectors. I
can determine if a set of vectors spans R^n.

I can state the definition of linear dependence and linear
independence. I can determine whether a set of vectors is linearly
independent or linearly dependent.

I have a conceptual understanding of the span of a set of vectors. For
example, I know how span(u, v) relates to span(u, v, 2u - 3v), how
span(u,v) relates to span(u+v, u), and how span (u,v) relates to
span(u,v,w) for some vector w. I understand the connection between
solving a linear system and determining if a vector is in the span of
other vectors.

I have a conceptual understanding of linear dependence and linear
independence. I can rephrase the definition of linear independence or
dependence in terms of span and in terms of solutions to linear
equations.

I understand the statement "The following are equivalent."