PERAN PEJABAT PEMBUAT KOMITMEN SEBAGAI PENGENDALI FUNGSI DALAM PEMBANGUNAN LANJUTAN LABORATORIUM B2P2TOOT TAWANGMANGU
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/wp.v2i2.12999
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Jurnal Wawasan Pendidikan
ISSN 2807-5714 (Print), ISSN 2807-4025 (Online)
Universitas Persatuan Guru Republik Indonesia Semarang
Jl. Sidodadi Timur No. 24 -Dr. Cipto, Semarang
Prasena Arisyanto, S.Pd., M.Pd
Email: prasenaarisyanto@upgris.ac.id
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License