Prove the second part of Theorem 6: Let w be any solution of Ax = b, and
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Prove the second part of Theorem 6: Let w be any solution of Ax = b, and define vh = w - p. Show that vh is a solution of Ax = 0. This shows that every solution of Ax = b has the form w = p + Vh, with p a particular solution of Ax = b and
Vh a solution of Ax = 0.
Data from in Theorem 6
Transcribed Image Text:
Suppose the equation Ax = b is consistent for some given b, and let p be a solution. Then the solution set of Ax = b is the set of all vectors of the form w = p + Vh, where V₁ is any solution of the homogeneous equation Ax = 0. Vh
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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