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Spring 2003 - Buss' Class - Exam 2

# Spring 2003 - Buss' Class - Exam 2 - Math 20F Linear...

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Math 20F - Linear Algebra Midterm Examination #2 – ANSWERS Spring, May 23, 2003 — Instructor: Sam Buss Write your name or initials on every page before beginning the exam. You have 50 minutes. There are 7 problems. You may not use notes, textbooks, calculators, or other materials during this exam. You must show your work in order to get credit. Good luck! Name: Student ID: Thursday section time: 1 2 3 4 5 6 7 Total

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Name: 2 1. a. State the deﬁnition of “the range of A , R ( A )”. ANSWER: { b : A x = b is consistent } b. State the deﬁnition of “ u 1 ,..., u k is a basis for U ”. ANSWER: u 1 u k are linearly independent and span U . c. State the deﬁnition of “ f : R n R m is a linear transformation”. ANSWER: For all x , y R n and all α, β R , f ( α x + β y )= αf ( x )+ βf ( y ) . d. State the deﬁnition of “ A represents the linear transformation f : R n R m ”. ANSWER: For all x R n , A x = f ( x ) . 2. Suppose that U is a subspace of R n and u 1 u k is a spanning set for U .
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Spring 2003 - Buss' Class - Exam 2 - Math 20F Linear...

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