Math 311-501, Topics in Applied Mathematics I (Spring 2012).

Material for test 1. (test given in class, 2/16/12)

Chapter 1: Sections 1,2,3.  
       Be able compute all solutions to 
           a linear system (or matrix vector problem) by setting up an
           argumented system and applying row operations.

Chapter 2: (in Sections 1)
     Be able to reduce determinants of nxn matrices to those of
          (n-1)x(n-1) matrices.
     Be able to compute determinants of 2x2 and 3x3.
     Be able to use basic properties such as determinant of a product =
        product of determinants,  nonsingular if and only if the
        determinant is nonzero, etc.

Chapter 3:  Sections 1,2,3,4.
     Be able to check when a subset of a vector space is a subspace.
     Know the definitions of linear independence, span and when 
          a set of vectors is a basis.
     Know how to determine whether a set of vectors span R^n.
     Know how to compute a basis for the null space of a matrix.
     Know how to express the range of a matrix as a span of vectors.
     Know how to extract a basis from a spanning set.