Cramer's Rule | ScienceGate

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.

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Membangkitkan Suatu Matriks Unimodular Dengan Python

Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika ◽

10.31316/j.derivat.v5i2.361 ◽

2018 ◽

Vol 5 (2) ◽

pp. 1-9

Author(s):

Samsul Arifin ◽

Indra Bayu Muktyas

Keyword(s):

Matrix Method ◽

Coefficient Matrix ◽

Inverse Matrix ◽

Solution Vector ◽

Unimodular Matrix ◽

All Solutions ◽

Cramer’S Rule

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

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An Earlier Date for “Cramer's Rule”

Historia Mathematica ◽

10.1006/hmat.1999.2247 ◽

1999 ◽

Vol 26 (4) ◽

pp. 365-368 ◽

Cited By ~ 3

Author(s):

Bruce A. Hedman

Keyword(s):

Cramer’S Rule

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Determinantal Representations of the Core Inverse and Its Generalizations with Applications

Journal of Mathematics ◽

10.1155/2019/1631979 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13 ◽

Cited By ~ 3

Author(s):

Ivan I. Kyrchei

Keyword(s):

Direct Method ◽

Linear Equations ◽

Close Relation ◽

Numerical Example ◽

Determinantal Representation ◽

The Core ◽

Core Inverse ◽

Cramer’S Rule ◽

The Right

In this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left core-EP inverses, and the DMP, MPD, and CMP inverses are derived by using determinantal representations of the Moore-Penrose and Drazin inverses previously obtained by the author. Since the Bott-Duffin inverse has close relation with the core inverse, we give its determinantal representation and its application in finding solutions of the constrained linear equations that is an analog of Cramer’s rule. A numerical example to illustrate the main result is given.

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