Math 311-501, Topics in Applied Mathematics I (Fall 2009).

Material for test 2. (test given in class, 11/3/09)

Chapter 3: Sections 4,6.

Chapter 5: Sections 1,2,3,4,5.
 

• You should know equivalent conditions for when an nxn matrix is nonsingular.
• Understand basis and dimension, e.g., what to do you need to check to see whether n vectors in R ⁿ are a basis.
• Row and column space, null space and rank. Be able to use Gaussian elimination to compute bases for row, column and null spaces.
• Be able to use Gaussian elimination to compute bases for the orthogonal complement of a subspace V of R ⁿ.
• Be able to set up least-squares problems.
• Be able to check whether a set of vectors are orthogonal and, if so, how to normalize them so that they are orthonormal.