Answered: The goal of this exercise is to find a…

The goal of this exercise is to find a least square solutions of a matrix equation Ax A = 2 0 2 0 2 7 = = b where 2 -3 1

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

a) Compute an orthogonal basis of the matrix A.

b) Use part a) to compute the vector projCol(A)b, i.e. the orthogonal projection of b onto the column space of A.

c) Solve the matrix equation Ax=projCol(A)b. Its solutions are the least square solutions of the original equation Ax=b.

The goal of this exercise is to find a least square solutions of a matrix equation Ax = b where
2 -2
41-8
0 0
b
-1 2
by calculating the projection of the vector b onto the column space of the matrix A.
A
=
=
2
-3

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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