Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 4 - Vector Spaces - Review Exercises - Page 223: 94

Answer

$$W =-2\sin^4x+2\cos^4 x. $$

Work Step by Step

$$W=\left| \begin {array}{ccc} x& \left( \sin \left( x \right) \right) ^ {2}& \left( \cos \left( x \right) \right) ^{2}\\ 1& 2\,\sin \left( x \right) \cos \left( x \right) &-2\,\sin \left( x \right) \cos \left( x \right) \\ 0&2\, \left( \cos \left( x \right) \right) ^{2}-2\, \left( \sin \left( x \right) \right) ^{2}&-2\, \left( \cos \left( x \right) \right) ^{2}+2\, \left( \sin \left( x \right) \right) ^{2}\end {array} \right|\\ =-2\sin^4x+2\cos^4 x. $$
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