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M118 Review 3 - Exam 3 Review Math 118 Sections 1 and 2...

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Exam 3 Review Math 118 Sections 1 and 2 This exam will cover sections 5.3-5.6, 6.1-6.3 and 7.1-7.3 of the textbook. No books, notes, calculators or other aids are allowed on this exam. There is no time limit. It will consist of 25 multiple choice questions. All exam questions will have the option ‘None of the above’, but when writing the exam, we intend to always include the correct answer. This means ’None of the above’ will be a correct answer only if there is a typo or similar type mistake. It is important that you know the terms, notations and formulas in the book. There are a disproportionate number of basic questions on this review, because almost all problems build on the knowledge of basic information. Some of the exam problems will mimic homework problems, but roughly 20% of exam questions will be what I call extension questions. See the last page section for a description and examples of extension questions. The review questions included are not all possible types of questions. They are just representative of the types of questions that could be asked to test the given concept. The following are the concepts which will be tested on this exam. A.1 Know how to determine the size of a matrix, and be familiar with the terminology associated with matrices: row, column, square matrix, row matrix, column matrix, row vector, col- umn vector, identity matrix (p.255), invertible matrix, inverse matrix, zero matrix (p. 268). Know the definition of matrix equality (p.239). Know when two matrices can be added and subtracted and how to add and subtract matrices. (5.3) A.2 Be able to multiply a scalar times a matrix. Know when two matrices can be multiplied and know how to multiply matrices.(5.4) A.3 Know the form and characteristics of the identity matrix. Know the definition and charac- teristics of an inverse matrix. Be able to calculate the inverse of a 2 × 2 or 3 × 3 matrix. (5.5) A.4 NOTE: You need to be comfortable with row operations and the Gauss Jordan method for this exam. A.5 NOTE: The (2 , 3) entry of a matrix is the entry in the second row and third column. 1. Use the matrices A = 1 2 1 0 0 1 , B = 1 2 0 2 3 4 , and C = 5 0 0 0 2 0 0 0 13 D = - 2 3 5 - 1 to do the following: (a) Find A T + B , if possible. (b) Find BA - 3 D , if possible. (c) Find the (3 , 1) entry of CB , if possible. (d) Find the (1 , 3) entry of A - 1 , if possible. (e) Find the (2 , 2) entry of D - 1 , if possible.
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