(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 6E
Related questions
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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70e1c88a-4b27-47b2-8d34-1f1fb2f12bbb%2Fdc5a5f0a-724b-49ff-84b4-e3f3ace03d09%2Fub1d9l_processed.png&w=3840&q=75)
Transcribed Image Text:(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).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra for College Students](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning