A system of linear equations in the variables x, y, z has the solution set S = {(x,y, z):x = t, y = 3s, z = 2t with s, te R} a) Is the system non-homogenous or homogenous? Justify your answer b) Determine a basis B for the subspace S of the real vector space R'. Then extend, if necessary, this basis to a basis C for R. Justify why B is a basis for S and C is a basis for R.

A system of linear equations in the variables x, y, z has the solution set S = {(x,y, z):x = t, y = 3s, z = 2t with s, te R} a) Is the system non-homogenous or homogenous? Justify your answer b) Determine a basis B for the subspace S of the real vector space R'. Then extend, if necessary, this basis to a basis C for R. Justify why B is a basis for S and C is a basis for R.

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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