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Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald
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Suppose the columns of A are linearly independent.

Chapter , Problem 10E

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QUESTION:

Suppose the columns of A are linearly independent. Determine what happens to the least-squares solution when b is replaced by cb for some nonzero scalar c.

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QUESTION:

Suppose the columns of A are linearly independent. Determine what happens to the least-squares solution when b is replaced by cb for some nonzero scalar c.

ANSWER:

Solution 10EStep 1 of 2The columns of are linearly independent.The system of equations is The set of all least –squares solutions coincides with the set of solutions of the normal equations The least square solution given by The solution of this equation exist when is invertible.Recollect that the matrix is invertible if and only if the columns of A are linearly independent.Since the matrix contains linearly independent columns, the solution exist.

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