Verify that the conclusion of Clairaut's theorem holds, that is, Uxy = Uyx" u = x5y8 - y5 With u = x5y8y5, we have the following. 5x4 U xy = Uyx = "y=40x4₂7 40x¹y7 = 8x5y7 - 5y4 × Since u xy X = U Clairaut's theorem holds for u = x5y8-y5. 'yx'
Verify that the conclusion of Clairaut's theorem holds, that is, Uxy = Uyx" u = x5y8 - y5 With u = x5y8y5, we have the following. 5x4 U xy = Uyx = "y=40x4₂7 40x¹y7 = 8x5y7 - 5y4 × Since u xy X = U Clairaut's theorem holds for u = x5y8-y5. 'yx'
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 20EQ
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Transcribed Image Text:Verify that the conclusion of Clairaut's theorem holds, that is, uxy = U.
"yx'
u = x5y8 - y5
With u = x
=
"y =
Uy
x5y8 - y5, we have the following.
=
Since u
4
5x
8x5y7 - 5y4x
Uyx 40x4y7
40x4y7
xy
X
x5y8 - y5.
= U Clairaut's theorem holds for u = x
"yx'
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