A Geometrical Proof of Cramer's Rule

1978 ◽  
Vol 9 (2) ◽  
pp. 106
Author(s):  
R. R. Baldino
1988 ◽  
Vol 19 (2) ◽  
pp. 171-171 ◽  
Author(s):  
Stephen H. Friedberg

1878 ◽  
Vol 9 ◽  
pp. 533-536
Author(s):  
Tait

In “Trans. R.S.E.” (1864–5) Fox Talbot proved very simply, by means of a species of co-ordinates depending on confocal conics, the following theorem, at the same time asking for a simple geometrical proof.If two sets of three concentric circles, with the same common difference of radii, intersect one another—the chords of the arcs intercepted on the mean circle of each series by the extremes of the other are equal.


Author(s):  
Nicoleta Mirela Marin ◽  
Gheorghe Batrinescu ◽  
Mihai Nita-Lazar ◽  
Luoana Florentina Pascu ◽  
Carol Blaziu Lehr

Two spectrometric methods have been developed for quantitative simultaneous determination of procaine hydrochloride (PH·HCl), procainamide hydrochloride (PHA·HCl) and lidocaine (Lid) from synthetic mixture. The methods employed are first derivative spectrometry, using zero crossing method and multicomponent analysis which is based on the additivity law. Using first derivative spectrometry, the wavelength selected for the quantitative determination of PH·HCl was 237 nm for Lid was 242 nm and for PHA·HCl was 290 nm in mixture. The method is linear when the concentration ranged between 6.62-9.93 μg/mL for PH·HCl, 6.43-9.64 for PHA·HCl and 5.56-8.35 for Lid. The multicomponent analysis is a direct method and involves the absorbance measurements of at three different wavelengths. The molar absorption coefficients values were calculated at each wavelength and the concentration of PH·HCl, PHA·HCl and Lid from mixture was determined by solving matrix using Cramer's rule. The recovery of each compound in mixture was calculated and it is 101.4 % for PH·HCl, 100.4 % for PHA·HCl and 98.4 % for Lid.


Author(s):  
Samsul Arifin ◽  
Indra Bayu Muktyas

An SPL can be represented as a multiplication of the coefficient matrix and solution vector of the SPL. Determining the solution of an SPL can use the inverse matrix method and Cramer's rule, where both can use the concept of the determinant of a matrix. If the coefficient matrix is a unimodular matrix, then all solutions of an SPL are integers. In this paper we will present a method of generating a unimodular matrix using Python so that it can be utilized on an SPL. Keywords: SPL, Unimodular Matrix, Python


1916 ◽  
Vol 20 ◽  
pp. 231-232
Author(s):  
Colin Kesson

Let ABC be the Δ, AD ⊥ to BC produced to meet circumcircle in K, BL a diameter of circumcircle, LM ⊥ to AK. Let BK, KG, CL and LA be joined.


1944 ◽  
Vol 34 ◽  
pp. 17-19
Author(s):  
J. H. M. Wedderburn

The usual proofs of Desargues Theorem employ either metrical or analytical methods of projection from a point outside the plane; and if it is attempted to translate the analytical proof by the von Stuadt-Reye methods, the result is very long and there is trouble with coincidences. It is the object of this note to give a short geometrical proof which, in addition to the usual axioms of incidence and extension, uses only the assumption that a projectivity which leaves three points on a line unchanged also leaves all points on it unchanged. Degenerate cases are excluded as having no interest.


1999 ◽  
Vol 26 (4) ◽  
pp. 365-368 ◽  
Author(s):  
Bruce A. Hedman
Keyword(s):  

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