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b. Find a specific vector u in V and a specific scalar c such that cu is not in V. Choose the correct answer below. O A. u= OB. u= -[3] 2 -2 O c. u= -2 c=1 c=4 | 0²-1 00. *-[-2]0-4 OD. u= c=4

b. Find a specific vector u in V and a specific scalar c such that cu is not in V. Choose the correct answer below. O A. u= OB. u= -[3] 2 -2 O c. u= -2 c=1 c=4 | 0²-1 00. *-[-2]0-4 OD. u= c=4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let V be the set of vectors shown below. V= x≤0, y ≤0 a. If u and v are in V, is u + v in V? Why? b. Find a specific vector u in V and a specific scalar c such that cu is not in V. a. If u and v are in V, is u + v in V? O A. The vector u + v may or may not be in V depending on the values of x and y. O B. The vector u + v must be in V because V is a subset of the vector space R². O C. The vector u + v must be in V because the x-coordinate of u + v is the sum of two nonpositive numbers, which must also be nonpositive, and the y-coordinate of u + v is the sum of nonpositive numbers, which must also be nonpositive. O D. The vector u + v is never in V because the entries of the vectors in V are scalars and not sums of scalars.
Transcribed Image Text:Let V be the set of vectors shown below. V= x≤0, y ≤0 a. If u and v are in V, is u + v in V? Why? b. Find a specific vector u in V and a specific scalar c such that cu is not in V. a. If u and v are in V, is u + v in V? O A. The vector u + v may or may not be in V depending on the values of x and y. O B. The vector u + v must be in V because V is a subset of the vector space R². O C. The vector u + v must be in V because the x-coordinate of u + v is the sum of two nonpositive numbers, which must also be nonpositive, and the y-coordinate of u + v is the sum of nonpositive numbers, which must also be nonpositive. O D. The vector u + v is never in V because the entries of the vectors in V are scalars and not sums of scalars.
b. Find a specific vector u in V and a specific scalar c such that cu is not in V. Choose the correct answer below. OA. u= OB. u= O c. u= OD. u= -2 -2 N N -2 2 -2 -2 c=1 c=4 | 0²-1 c=4
Transcribed Image Text:b. Find a specific vector u in V and a specific scalar c such that cu is not in V. Choose the correct answer below. OA. u= OB. u= O c. u= OD. u= -2 -2 N N -2 2 -2 -2 c=1 c=4 | 0²-1 c=4
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