MATH 3100 final exam study guide

The final exam for MATH 3100 is Wednesday, Dec 12.  The exam will cover material from the
entire course, with an emphasis on material we've covered since the second exam.  So, the new sections (since Exam 2) will be: Sections 4.1, 4.2, 4.4, 5.1, 5.2, and 6.1-6.3.
Problems will similar to homework problems, and the following practice problems from 6.2 & 6.3:

 p.341-342 #3, 9, 15, 27 and p.353-354 #9, 13, 15, 25

There won't be any questions about MATLAB or Section 4.6.
 
Like the other exams, you are welcome to bring a calculator and a 3x5 notecard (both sides).

Here's a list of topics you should be familiar with:

Linear systems
Row operations
  Row echelon form
  Reduced row echelon form
Matrix operations
  Inverse
  Transpose
  Determinant
LU factorization
Vector spaces
Linear combinations
Linearly independent vectors
Subspaces
  Span of a set of vectors
  Null space of a matrix
  Column space of a matrix
Basis of a vector space/ subspace
  Dimension
Change of basis
Linear transformations
  Null space of transformation
  Range of a transformation
Matrix representations for transformations
Eigenvalues and Eigenvectors
  for matrices
  for linear transformations
Diagonalization of matrices
Inner product spaces
  Dot product
  Abstract inner product
  Orthogonality
Orthonormal bases
  Gram-Schmidt