If A is a rectangular matrix with more columns than rows and for some r.h.s. b, we can find a particular solution of Ax = b, i.e., for some vector xp, we have Axp = b. How many solutions would Ax = b have? How can we describe all the solutions of Ax = b?

If A is a rectangular matrix with more columns than rows and for some r.h.s. b, we can find a particular solution of Ax = b, i.e., for some vector xp, we have Axp = b. How many solutions would Ax = b have? How can we describe all the solutions of Ax = b?

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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Question

If A is a rectangular matrix with more columns than rows and for some r.h.s. b,
we can find a particular solution of Ax = b, i.e., for some vector xp, we have
Axp = b. How many solutions would Ax = b have? How can we describe all the
solutions of Ax = b?

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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