Show that the determinant of the Jacobian matrix of Mapping (9.... | Filo

How to Find the Determinant of a Matrix | Precalculus | Study.com

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SOLVED: Calculate the Jacobian matrix [J] for the transformation from natural (X,y) coordinates to intrinsic (€ n) coordinates for the element shown in Figure 2b.Where: x = 1 35 39 35y = 3n n(5 marks)3(6,4)4(-2,2)4(-1,1)3(1,1)1(-1,1)2(1,-1)(-2,-2)2(4,-4)Natural coordinatesIntrinsic coordinatesFigure 2bThe Jacobian Matrix [J] is given by:dx dyag 05dx Jdn dv

Finding the Determinant of a Matrix | Properties, Rules & Formula

SOLVED: (10 marks)A 4-noded quadrilateral element is shown in Figure 1. The unit of the coordinates X and y is in mm. Determine the Jacobian matrix [J] for the element:4 (-1, 4)3 (4, 1)1 (-2, -1)2 (1, -1)Note: The shape functions for a 4-noded quadrilateral element in intrinsic coordinates are given by:N1 = (X-1)(4-y)/4, N2 = (1 X)(1-y)/4, N3 = (1 X)(1 y)/4, N4 = (1-X)(1 y)/4The Jacobian matrix [J] is defined as follows:[J] = [dx/dX, dx/dy] [dy/dX, dy/dy]Figure 1