Math 210-01: Linear Algebra: Reading Homework 3.3--4

1. Properties of Determinants :
   
   1. Products : what is the determinant of a product of matrices? of a scalar and a matrix?
      
   2. Invertibility : when is a matrix invertible? how is the determinant of the inverse related to that of the original matrix?
      
      1. conditions : what statements are equivalent to that of ``a matrix is invertible''?
         
      2. eigenvalues : what is the equation of an eigenvalue problem? how can we find the eigenvalue?
         
2. Applications of Determinants :
   
   1. Adjoints and inverses : how is the adjoint of a matrix related to its cofactors? how is the inverse related to the adjoint?
      
      1. practicality : is this a way that we would commonly calculate an inverse?
         
   2. Cramer's rule : what does Cramer's rule do?
      
   3. Area and Geometry :
      
      1. triangles : how is the area of a triangle related to determinants?
         
      2. collinear points : how can we determine if three points are collinear? how is this related to the area of a triangle?
         
      3. lines : how is the equation of a line in the plane related to determinants?
         
      4. three dimensions : how do the preceding three results generalize to three dimensions?