This exam is cumulative, so be sure to study the older chapters that were covered in the first and second midterm exams. It is also essential that you look over your old exams (and quizzes and homework) to avoid repeating mistakes you may have made before. The information here 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).
6.1: You should know all the definitions and theorems in this chapter. You do not need to know the section on computing average class size.
6.2: You should know what an orthogonal/orthonormal set is, and how to write a vector as a linear combination of vectors in an orthogonal set using dot products. You definitely need to know the Gram-Schmidt process. We did not cover QR factorizations, and they will not be included in this exam.
6.3: You should know how to find the orthogonal complement of a set or subspace, and how to find the orthogonal projection onto a subspace. Make sure you know how to find a projection matrix!
6.4: You should know to find the least squares line for a set of data, and the error minimizing solution to an inconsistent system of linear equations. You can ignore the section on solutions of least norm.
6.5: You should know what orthogonal matrices are along with their properties. The section on rigid motions is not included.
6.6: You should know what symmetric matrices are, and how to find a spectral decomposi- tion for them. We did not cover quadratic forms, and they will not be included on this exam.
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