MATH 241 Midterm: MATH 241 UIUC Math241_Fall08_2PM_Exam1

• School: University of Illinois
• Department: Mathematics
• Course: MATH 241
• Professor: All

Document Summary

Math 241 exam 1 2pm v1. ||a + b|| ||a|| + ||b||: let a = 4. 0 5 (a) (3pts) consider the function f (~x) = a~x, f : rn rm. Clearly explain what the values of m and n are. (b) (c) (3pts) let ~a = (1, 2, 3). Compute f (~a). (4pts) explain why the function f is a linear transformation. (5pts) find an equation of the plane containing the points ( 1, 0, 4), (1, 5, 2) and. 2. (2, 4, 8): let f (x, y) = 2x2 3y2. (a) (b) answer. (3pts) draw three level sets of this function. Math 241 exam 1 2pm v2. 2 2 (a) (3pts) consider the function f (~x) = a~x, f : rn rm. Clearly explain what the values of m and n are. (b) (c) (3pts) let ~a = ( 1, 3).