Let { d1, . . , di } be directions of unboundedness for the constraints Ax = b, x > 0. Prove that k d = ) `a;d; with a; > 0 i=1 Is also a direction of unboundedness for these constraints.
Let { d1, . . , di } be directions of unboundedness for the constraints Ax = b, x > 0. Prove that k d = ) `a;d; with a; > 0 i=1 Is also a direction of unboundedness for these constraints.
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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![**Exercise 4.5**
Let \(\{d_1, \ldots, d_k\}\) be directions of unboundedness for the constraints:
\[ Ax = b, \quad x \geq 0. \]
Prove that
\[ d = \sum_{i=1}^{k} \alpha_i d_i \quad \text{with} \quad \alpha_i \geq 0 \]
is also a direction of unboundedness for these constraints.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbffa73e6-1761-4c9e-97cb-0c164f013989%2Fd9fbab7c-b09a-4763-81e7-47bc278cbfa6%2Fflhnwimr_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise 4.5**
Let \(\{d_1, \ldots, d_k\}\) be directions of unboundedness for the constraints:
\[ Ax = b, \quad x \geq 0. \]
Prove that
\[ d = \sum_{i=1}^{k} \alpha_i d_i \quad \text{with} \quad \alpha_i \geq 0 \]
is also a direction of unboundedness for these constraints.
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