Problem 3. Let A be the linear transformation from R" to Rm. Define AC = {Ax|x = C'} and A-¹D = {x| Ax € D}. Show that if C and D are convex, then AC and A-¹D are still convex.
Problem 3. Let A be the linear transformation from R" to Rm. Define AC = {Ax|x = C'} and A-¹D = {x| Ax € D}. Show that if C and D are convex, then AC and A-¹D are still convex.
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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Transcribed Image Text:Problem 3.
Let A be the linear transformation from R" to Rm. Define
AC = {Ax|x € C'} and A-¹D = {x| Ax € D}. Show that if C and D are convex, then
AC and A-¹D are still convex.
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