Implementation of Building Information Modelling (BIM 3D) on the Steel Building project: Case study of the 3-storey building GKJ MARGOYUDAN

Kukuh Kurniawan Dwi Sungkono, Ronald Sukwadi

Abstract


This study investigates the general form of the determinant of negative integer powers of a special class of centrosymmetric matrices of even order. For an even positive integer and a positive integer , let denote such a matrix, and consider the matrix obtained by raising to the power . To determine , we first conjecture the general form of the inverse matrix by observing the patterns in the explicit inverses , and . The conjectured form is then verified by showing that and . The resulting inverse is used to construct the matrices , and ; from these cases we infer the general structure of . The validity of this general form is established using mathematical induction. Once the matrix has been obtained, an explicit closed-form expression for is derived via the cofactor expansion method. Finally, a numerical example is presented to illustrate the application of the determinant formula.


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DOI: https://doi.org/10.26877/ijosbie.v3i2.13518

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