2. Let u-("і "2,W3), ν (η , v 2, vs), and w-( w. w2,W3 ) be three vectors in R. Recall that the oriented volume V(u,v,w) of the parallelepiped spanned by u,v,w equals (их v) . w (See p. 45 for the definition of the cross product.) (b) If A is a 3 x 3-matrix, prove that V(Au,Av,Aw)-det(A)V(u, v, w). Remark. The formula from (b) shows that det(A) measures how the linear transforma tion with matrix A changes the volume of a region in R5.
2. Let u-("і "2,W3), ν (η , v 2, vs), and w-( w. w2,W3 ) be three vectors in R. Recall that the oriented volume V(u,v,w) of the parallelepiped spanned by u,v,w equals (их v) . w (See p. 45 for the definition of the cross product.) (b) If A is a 3 x 3-matrix, prove that V(Au,Av,Aw)-det(A)V(u, v, w). Remark. The formula from (b) shows that det(A) measures how the linear transforma tion with matrix A changes the volume of a region in R5.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.4: Relationships: Perpendicular Lines
Problem 27E
Related questions
Question
Please help!
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,