2. Consider the following sets of vectors. Show that each set (i) contains the zero vector, (ii) is closedunder addition and scalar multiplication. Then find a basis for each set and give the dimension.(a) W is the set of vectors of the form (3s, -2s, s).(b) W is the set of vectors of the form (t – 2, 0,6 – 3t).(c) H is the set of vectors of the form (2b, a, 3b)(d) H is the set of vectors of the form (-b+ 2c, b, 4c),

The given sets are (a) W is the set of vectors of the form 3s, -2s, s. We have to show that i Each…

Answered: 2. Consider the following sets of…

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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2. Consider the following sets of vectors. Show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. Then find a basis for each set and give the dimension. (a) W is the set of vectors of the form (3s, -2s,s).