The following is a chapter by chapter guide intended to help you organize the material we have covered in class as you study for your exam. It is only intended to serve as a guidline, and may not explicitly mention everything that you need to study. Please review all homework, quiz and example problems for the chapters given below (including the true/false problems). I have also compiled a list of additional practice problems.
1.1 & 1.2: You should definitely know all the definitions and properties covered in these sections. All other chapters use these concepts implicitly, so make sure you are comfortable with the material in these chapters.
1.3: You should know how to find the general solution for a system of linear equations, and the conditions for getting a unique solution, infinitely many solutions, or no solutions.
1.4: This is the most important chapter for us. You need to know Gaussian elimination for all of the subsequent chapters, and you need to understand row echelon form and reduced row echelon form. You also need to know the rank-nullity theorem.
1.6: You should understand what the span of a set is, and you should know the theorems in this chapter well.
1.7: You must know what it means for a set of vectors to be linearly independent, and you should definitely know the information contained in Theorem 1.8, as well as the properties listed on p. 81. The table on p. 83 is a useful summary of the material covered in Sections 1.6 and 1.7.
2.1: You should be very comfortable multiplying matrices (and determining when the product does not exist). You should also know all the properties listed in Theorem 2.1 and all the types of matrices defined on p. 103.
2.3: You should understand elementary matrices, and how multiplication by an elementary matrix is equivalent to performing row operations. Make sure you can distinguish between an elementary matrix and the product of elementary matrices. You should also understand invertibility, its properties, and how it is used to solve systems of linear equations. You should be able to write down the inverse of an elementary matrix by considering the inverse elementary row operation.
2.4: You should know how to determine whether a matrix is invertible, and how to find the inverse if it is. Pay attention to the Invertible Matrix Theorem.
2.5: You should know how to multiply a matrix in blocks, although you will not be required to partition a matrix into blocks yourself. (However, you welcome to do so if you find it convenient.)
2.6: We are only covering pages 152-158 of this section. You should know how to find the LU-decomposition of a matrix if it exists, and how to use this to solve linear systems of equations.
Maintained by ynaqvi and last modified 02/24/13