Standards: Chapter 4

I can prove whether or not a subset W of a vector space V forms a
subspace. I can determine and characterize subspaces of R^n. I have a
geometric understanding of what subspaces look like in R^2 and R^3.

I can write a proof showing whether a subset of vectors from a
subspace forms a spanning set for the subspace (or not). I can write a
proof to show whether a subset of vectors from a subspace is linearly
independent (or not). I can determine whether a set of vectors forms a
basis for a subspace. I can find the dimension of a subspace. I can
identify a basis for R^2 and R^3 pictorally.

I can find a basis for the row space, the column space, or the null
space of a matrix. I can determine the rank and nullity of a
matrix. Given a consistent system Ax=b, I can describe the general
solution in the form x=x_p+x_h.

I can find a basis for the kernel and range of a linear
transformation. I can rephrase statements about a linear
transformation being one-to-one or onto in terms of statements about
the kernel and range.