This is a first course in linear algebra which is less
theoretical and more oriented towards applications than 
Introduction to Linear Algebra.  Students should understand the 
concepts of vector spaces, bases, linear transformation, and 
matrix algebras. 
Students should be able to do the following:
(1) Solve systems of linear equations by means of Gaussian
elimination
(2) Calculate the inverse of a matrix
(3) Determine the projection operator onto a subspace
(4) Determine the null space and range space of a linear
transformation
(5) Calculate the eigenvalues and eigenvectors of a matrix
(6) Calculate the singular value decomposition of a matrix
(7) Use linear algebra in problems of science and engineering

1. Vector algebra. Dot products.  Matrices.
2. Solving linear equations using elimination.
3. Matrix algebra: product, inverse, and transpose.
4. Subspaces: nullspace, rowspace, column space of a matrix.
5. Linear independence, basis, and dimension, orthogonal 
complement. 
6. Orthogonality. Projections and least-squares
approximation. Gram-Schmidt process. Change of basis formula.
7. Determinants. Cramer's rule.
8. Eigenvalues and eigenvectors, diagonalizability.  Singular
value decomposition.
9. Applications to science and engineering, including topics 
such as networks, Markov processes, linear programming, 
statistics, computer graphics.