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3e-spring2011-exam_1_review - • Add matrices • Multiply...

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Math 3E — Exam #1 Review Laney College, Spring 2011 Fred Bourgoin Exam #1 will cover chapters 1 and 2. The following is a list of topics you need to be familiar with for the exam. Even though calculators are allowed on the exam, remember that you will only earn the full credit if you show all your steps. Solutions to the True/False questions at the end of the chapters are posted on the website. Chapter 1: Linear Equations Find the reduced row-echelon form of a matrix using Gauss-Jordan elimina- tion. Solve a linear system using augmented matrices and Gauss-Jordan elimination. Recognize when a linear system has no solutions. Recognize when a linear system has infinitely many solutions, and write the solutions using parameters ( s , t , etc.). Recognize when a linear system has exactly one solution. Interpret a linear system geometrically. Solve simple applications problem (like #20, 21, 24, 27, 29–37, 44, 46–48 in section 1.1, and #30, 31, 33, 37, 42, 44, 62–64 in section 1.2).
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Unformatted text preview: • Add matrices. • Multiply a matrix by a scalar. • Multiply a matrix by a vector. • Find the dot product of two vectors. • Write a linear system in matrix/vector form. • Know what a linear combination is, and be able to determine whether a given vector can be written as a linear combination of a set of vectors. Chapter 2: Linear Transformations • Know what a linear transformation is, and be able to recognize whether a given function is a linear transformation. • Find the matrix for a linear transformation (see p. 47). • Know the properties of linear transformations, and be able to verify them in an example. • Scale, project, reflect, and rotate vectors in R 2 . • Determine whether a given matrix is invertible, and find its inverse. • Multiply matrices. • Know and apply the properties of matrix multiplication....
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