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Unformatted text preview: Midterm Problems MAT26500 - 11,12 Here is a collection of problems to prepare for the midterm. I suggest you use the textbook to supplement your study. In particular, you should answer all the True/False questions at the end of each chapter (at least the ones that apply to the sections we covered, which is nearly all of them), and perhaps some of the Supplementary Exercises. For example, I would suggest having a look at; 1. Chapter 1 Supplementary exercises: 2, 4 , 6, 14, 19a, 19b, 23 (these are not typical of the problems that will appear on the exam, but theyre not bad problems to look at) 2. Chapter 2 Supplementary exercises: 1, 2, 3, 7, 8, 11, 12, 13 (since we never discussed elementary matrices you can ignore any questions about them) 3. Chapter 3 Supplementary exercises: 1, 2, 3, 4, 8, 9* 4. We have only started chapter 4 so you can ignore that part It appears these supplementary exercises tend to be more difficult, so do not be terribly alarmed if you have some difficulty with some of them. The problems on the exam will tend to be more like the ones below. Problem 1. Consider the matrix 1 5 7 21 1 3 1 5 1 3 1 12 1 2 17 1. Is this matrix in row echelon form? In reduced row echelon form? (Both? Neither?) 2. How many solutions to the corresponding linear system are there (interpret the matrix as the augmented matrix for a linear system)? 3. Assume the variables are name x 1 ,...,x k . What is k (i.e. how many variables are there)? Which variables correspond to parameters (are free variables)? Which variables are determined by these parameters (free variables)? Problem 2. Consider the matrix 1 3 2 1 2 1 1 Is this matrix in row echelon form? In reduced row echelon form? How many solutions to the corresponding linear system are there (interpret the matrix as the augmented matrix for a linear system)? Problem 3. Consider the linear system x 1 +2 x 2 x 3 + x 4 = 2 7 x 1 +14 x 2 5 x 3 + x 4 = 1 2 x 1 3 x 2 +6 x 3 x 4 = 3 1. Determine how many solutions this system has....
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