by using its echelon form. 3. Let X = (ij) be an nxn matrix with variable entries, and consider the function F(x) = det X as a polynomial with real coefficients in the variables Tij. For each (i, j) prove that the partial derivative F equals (-1)+j det Xij, the (i, j)-cofactor of X. dzij

by using its echelon form. 3. Let X = (ij) be an nxn matrix with variable entries, and consider the function F(x) = det X as a polynomial with real coefficients in the variables Tij. For each (i, j) prove that the partial derivative F equals (-1)+j det Xij, the (i, j)-cofactor of X. dzij

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 48RE

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Question

by using its echelon form.
3. Let X = (ij) be an nxn matrix with variable entries, and consider the function F(x) = det X
as a polynomial with real coefficients in the variables Tij. For each (i, j) prove that the partial derivative
F equals (-1)+j det Xij, the (i, j)-cofactor of X.
dzij

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