Calendar

Please note that the homework dates denote the due dates of the homework.

The sections will be covered on the days noted.

Homework is collected in class on the due date.

A short quiz, covering the noted sections, will be given these days.

The following exams will be given.

What follows is a rough study guide for the midterm. This may see minor refinements after I write the test.

You should be familiar with all of the theorems and homework problems in the sections for which we had homework up through and including 4.5. The following is a list of a few of the key concepts covered in the material and homework problems. The list is not a comprehensive list of everything you will be tested over, but should be a good guide.

Calculators/computers will not be allowed on the midterm.

1. Systems of linear equations
   1. Set up problems involving a linear system of equations
   2. consistency of a system and uniqueness of solutions
   3. geometry associated with the solutions to a system
   4. converting between matrix*vector, linear combination of vectors, and list of equations forms of writing a system of equations
   5. solving systems of linear equations using row reduction and inverse matrices, writing the answer as a set of equations or in parametric form (i.e., as a linear combination of vectors possibly plus a constant vector)
   6. Homogeneous systems of equations and how they and their solutions are related to corresponding nonhomogeneous systems, the geometry of homogeneous and nonhomogeneous systems
2. Matrices
   1. Row echelon form: row-reduce a matrix to echelon and/or reduced echelon form, identify pivot positions, pivot columns, basic variables, and free variables
   2. Understand matrix multiplication and five ways to interpret it (see p. 136)
   3. Properties of matrix operations (e.g., transpose, multiplication is not commutatitive, etc.)
   4. Finding and working with matrix inverses; testing for invertibility; the invertible matrix theorem
   5. Working with partitioned matrices (multiplication, inverses, etc.)
   6. Determinants: finding using cofactor expansion and using row reduction; know how row operations affect the determinant; testing invertibility and linear indepenence using determinants, other properties of determinants in 3.1 and 3.2.
3. Vectors
   1. Linear combinations: determining when a vector is in the span of other vectors; know what being in the span of vectors means geometrically.
   2. Linearly independent sets of vectors: determining a set of vectors is linearly independent using row reduction; know what a linearly independent set means geometrically.
4. Linear transformations
   1. Know about range, kernel, domain, codomain, one-to-one, onto, image, preimage
   2. Finding vectors in the range of a linear transformation
   3. Finding the matrix of a linear transformation given a geometric or algebraic description of the transformation or a description of the images of the standard basis vectors.
5. Vector spaces
   1. Definitions and examples of vector spaces
   2. Determining if a set of vectors is a subspace.
   3. The nullspace, column space, and row space of a matrix; finding a matrix with a given column or row space; testing if a vector is in the nullspace or column space; what the column space and nullspace represent geometrically when you think of the matrix as a linear transformation.
   4. Bases: What a basis is; finding a basis for a vector space (including column spaces, nullspaces, and row spaces using row reduction, as well as for spaces other than R^n), determining if a set of vectors is a basis, the relationship between bases, spanning sets, and linearly independent sets
6. Other material from 4.4 and 4.5