(a) Let u,v and w be vectors in R³. The volume(u, v, w) is given by determinant of [u v w]. (i) Derive the volume(4u +v, u+2w, –3v+w) in terms of volume(u, v, w). (ii) Hence, compute the volume(4u + v,u+2w, –3v + w) when u = (2,1,1), v = (1,2,0) and w= (1,0, 1).

(a) Let u,v and w be vectors in R³. The volume(u, v, w) is given by determinant of [u v w]. (i) Derive the volume(4u +v, u+2w, –3v+w) in terms of volume(u, v, w). (ii) Hence, compute the volume(4u + v,u+2w, –3v + w) when u = (2,1,1), v = (1,2,0) and w= (1,0, 1).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 8E

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Question

question a) ii)

(a)
Let u, v and w be vectors in R³. The volume(u, v, w) is given by determinant of
[u v w].
(i)
Derive the volume(4u+v, u+2w, –3v+w) in terms of volume(u, v, w).
(ii)
Hence, compute the volume(4u + v,u+2w, –3v+ w) when u = (2,1,1),
v= (1,2,0) and w= (1,0,1).

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