Cofactor Matrix | Definition, Calculation & Use

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

A Jacobian matrix and two equlibria are given. Determine if each is locally stable, unstable, or if the analysis is inconclusive. J=[ 2 x1 -sin x2 cos x1 0] (i) x̂1=1, x̂2=-π(ii) x̂1=1, x̂2=π | Numerade

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

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