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_3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex combination of { yi,1, the vectors { yi, j }. ... Yi,k; }. Prove that x is a convex combination of .. ,

_3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex combination of { yi,1, the vectors { yi, j }. ... Yi,k; }. Prove that x is a convex combination of .. ,

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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**4.3.** Let \( x \) be a convex combination of \(\{ y_1, \ldots, y_k \}\). Assume in turn that each \( y_i \) is a convex combination of \(\{ y_{i,1}, \ldots, y_{i,k_i} \}\). Prove that \( x \) is a convex combination of the vectors \(\{ y_{i,j} \}\).
Transcribed Image Text:**4.3.** Let \( x \) be a convex combination of \(\{ y_1, \ldots, y_k \}\). Assume in turn that each \( y_i \) is a convex combination of \(\{ y_{i,1}, \ldots, y_{i,k_i} \}\). Prove that \( x \) is a convex combination of the vectors \(\{ y_{i,j} \}\).
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