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a. Show that the null-space N(A) is a convex set. Is it true for every A?

a. Show that the null-space N(A) is a convex set. Is it true for every A?

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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Problem 6: Consider a full rank m x n matrix A with m < n. a. Show that the null-space N(A) is a convex set. Is it true for every A? b. Now, suppose we have been provided with a vector y € R". We want to find another vector x* which is closest (in terms of l2 norm) to y such that x* € N(A). Formulate the problem in terms of constrained optimization problem sing appropriate Lagrangian, and solve it to find x*. You are NOT allowed to directly use right-pseudoinverse formulae here in any way.
Transcribed Image Text:Problem 6: Consider a full rank m x n matrix A with m < n. a. Show that the null-space N(A) is a convex set. Is it true for every A? b. Now, suppose we have been provided with a vector y € R". We want to find another vector x* which is closest (in terms of l2 norm) to y such that x* € N(A). Formulate the problem in terms of constrained optimization problem sing appropriate Lagrangian, and solve it to find x*. You are NOT allowed to directly use right-pseudoinverse formulae here in any way.
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