Modern Method to Compute the Determinants of Matrices of Order 3

Ali A.M. Ahmed, K. L. Bondar

Abstract


In this paper we present new method to compute the determinants of $3 \times 3$ matrices. This method gives an easy schemes to compute the determinants of $3 \times 3$ matrices. It also gives fast approximation as we described only five elements of the determinant. This new method creates opportunities to find other new method to compute the determinants of higher orders, also.

Keywords


Methods to compute the determinant of $3\times 3$ matrix

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References


S. Barnard, J. M. Child, Higher Algebra, London Macmillan LTD New York, ST Martins Press (1959), 131.

F. Chió, Mémoire sur les fonctions connues sous le nom de résultantes ou de determinants, Turin: E. Pons, 1853.

C.L. Dodgson, Condensation of Determinants, Being a New and Brief Method for Computing their Arithmetic Values." Proc. Roy. Soc. Ser. A 15, (1866),150-155.

H. Eves, Chio's Expansion, §3.6 in Elementary Matrix Theory, New York: Dover, (1996), 129-136.

W. L. Ferrar, Algebra, A Text-Book of determinants, matrices and algebraic forms, Second edition, Fellow and tutor of Hertford College Oxford, (1957), 7.

D. Hajrizaj, New Method to Compute the Determinant of $3 times 3$ Matrix, International Journal of Algebra, Vol. , (2009), 211-219.

H. Ejup, Matematika 1, Universiteti i Prishtinës: Fakulteti Elektroteknik, Prishtinë, (2000), 163-164.

H. P. Henry, An elementary treatise on the theory of determinants. A textbook for colleges, Ithaca, New York: Cornell University Library, Boston, Ginn and Company (1886), 13, 14, 18.

J. V. Collins, Advanced algebra, American Book Company(1913), 281, 286.

R. F. Scott, The theory of determinants and their applications, Ithaca, New York, Cornell University Library, Cambridge: University Press, (1904), 3-5.

L. G. Weld, A short course in the theory of determinants, Ithaca, New York: Cornell University Library, New York, London: Macmillan and Co (1893), 8.

L. G. Weld, Determinants, Ithaca, New York, Cornell University Library, New York, J. Wiley and Sons (1906), 14-15.




DOI: http://dx.doi.org/10.26713%2Fjims.v6i2.243

eISSN 0975-5748; pISSN 0974-875X