3. Let W be defined asx + 4y + 5z2.x – y + zW =| x, y, z E RЗх + Зу + 626х + 6у + 12z(i) Show that W is a subspace of R4(ii) Find a spanning set for W.(iii) Find a basis for W.(iv) Extend the basis above to a basis for Rª.(v) Find a complement of W in R4.

Using extension theorem to get a basis of vector space. Here the complement may or may not be…

Answered: 3. Let W be defined as x + 4y + 5z 2x –…

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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3. Let W be defined as x + 4y + 5z 2x – y + z Зх + 3у + 62 6х + 6у + 122, W = |x, y, z E R (i) Show that W is a subspace of Rª (ii) Find a spanning set for W. (iii) Find a basis for W. (iv) Extend the basis above to a basis for Rª. (v) Find a complement of W in R4.