Math 210-01: Linear Algebra: Reading Homework 3.3--4
- Properties of Determinants :
- Products : what is the determinant of a product of matrices? of a scalar and a matrix?
- Invertibility : when is a matrix invertible? how is the determinant of the inverse related to that of the original matrix?
- conditions : what statements are equivalent to that of ``a matrix is invertible''?
- eigenvalues : what is the equation of an eigenvalue problem? how can we find the eigenvalue?
- Applications of Determinants :
- Adjoints and inverses : how is the adjoint of a matrix related to its cofactors? how is the inverse related to the adjoint?
- practicality : is this a way that we would commonly calculate an inverse?
- Cramer's rule : what does Cramer's rule do?
- Area and Geometry :
- triangles : how is the area of a triangle related to determinants?
- collinear points : how can we determine if three points are collinear? how is this related to the area of a triangle?
- lines : how is the equation of a line in the plane related to determinants?
- three dimensions : how do the preceding three results generalize to three dimensions?
Math 210-01: Linear Algebra: Reading Homework 3.3--4
Last Modified: Mon Feb 8 01:07:25 1999
Comments to: glarose@umich.edu