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The tetrahedron defined by three vectors 5i, 52,53 in R3 is the set of all vectors of

Linear Algebra with Applications | 4th Edition | ISBN: 9780136009269 | Authors: Otto Bretscher ISBN: 9780136009269 434

Solution for problem 5 Chapter 6.3

Linear Algebra with Applications | 4th Edition

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Linear Algebra with Applications | 4th Edition | ISBN: 9780136009269 | Authors: Otto Bretscher

Linear Algebra with Applications | 4th Edition

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Problem 5

The tetrahedron defined by three vectors 5i, 52,53 in R3 is the set of all vectors of the form c\v\ + C2V2 + C3U 3, where c,- > 0 and c\ + C2 + C3 < 1. Explain why the volume of this tetrahedron is one-sixth of the volume of the parallelepiped defined by 5j, 52, 53.

Step-by-Step Solution:
Step 1 of 3

Zo:r\ttl f-\>urro-\*Ve: licr ' \-"l ;\ Lx rdx*-a {*C X_ \ ,;1'A /Y\n \ LO,D L.) rl rA (il ;\ x inl {J , re ,D] *a I "-\ ( )(. x.-'L) -\ \i,2 \ -'€'A1 ''.) f I / t I VR'k= I x-\ (\x--tOx--Uf .-tK.--x\I nn MNL x -)fi LCIx+\ l.r-r-..-r^l /1 +Lx ), dr:x{ Q)

Step 2 of 3

Chapter 6.3, Problem 5 is Solved
Step 3 of 3

Textbook: Linear Algebra with Applications
Edition: 4
Author: Otto Bretscher
ISBN: 9780136009269

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The tetrahedron defined by three vectors 5i, 52,53 in R3 is the set of all vectors of