How do you compute the Jacobian of a transformation that takes the variables (x, y) into the variables (r,t)? dr dr дх ду · Ət ət- LƏx dy. Form the determinant of a 2 × 2 matrix whose first row is and whose second row is - Əx dx- dr Ət] гду ду Form the determinant of a 2 × 2 matrix whose first row is and whose second row is now take absolute value. ər dt dr dr Ət dt Form the determinant of a 2 × 2 matrix whose first row is and whose second row is now take absolute value. dx dy dx dy. ây dy Form the determinant of a 2 × 2 matrix whose first row is and whose second row is dr dt

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 34E
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How do you compute the Jacobian of a transformation that takes the variables (x, y) into the variables (r,t)?
dr dr:
Əx dy!
· Ət dt
Lдх ду.
Form the determinant of a 2 × 2 matrix whose first row is
and whose second row is
[dy dy
Ər dt
Form the determinant of a 2 × 2 matrix whose first row is
and whose second row is
now take absolute value.
dr dt.
dr dr
Əx dy!
at dt
Form the determinant of a 2 × 2 matrix whose first row is
and whose second row is
now take absolute value.
dx dx
гду дут
Lər ôt
Form the determinant of a 2 × 2 matrix whose first row is
and whose second row is
Ər dt
Transcribed Image Text:How do you compute the Jacobian of a transformation that takes the variables (x, y) into the variables (r,t)? dr dr: Əx dy! · Ət dt Lдх ду. Form the determinant of a 2 × 2 matrix whose first row is and whose second row is [dy dy Ər dt Form the determinant of a 2 × 2 matrix whose first row is and whose second row is now take absolute value. dr dt. dr dr Əx dy! at dt Form the determinant of a 2 × 2 matrix whose first row is and whose second row is now take absolute value. dx dx гду дут Lər ôt Form the determinant of a 2 × 2 matrix whose first row is and whose second row is Ər dt
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