Pre-service mathematics teachers’ mental constructions when using Cramer’s rule
South African Journal of Education, 2019 This study explored the mental constructions displayed by pre-service mathematics teachers (PMTs) when applying Cramer’s rule. The aim was to reveal the character of mental constructions made around the nature of the solution set of equations and the ...
Zanele Ndlovu, Deonarain Brijlall
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Types of System of the neutrosophic linear equations and Cramer’s rule [PDF]
Neutrosophic Sets and Systems, 2021 The purpose of this article is studying the types of system of neutrosophic linear equations, where the neutrosophic linear equation and the solution to the neutrosophic linear equation are defined.
Yaser Ahmad Alhasan
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On application of Cramer’s rule
Lietuvos Matematikos Rinkinys, 2011 The article analyses a possibility of modification of Cramer’s rule. The modified formulas for the solution of a system of linear equations, with application of which the volume of calculation reduces, are suggested.
Antanas Apynis
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Characterizations of the Generalized MPCEP Inverse of Rectangular Matrices
Journal of Applied Mathematics, 2023 In this paper, we introduce a new generalized inverse, called the G-MPCEP inverse of a complex matrix. We investigate some characterizations, representations, and properties of this new inverse.
Jiaxuan Yao, Xiaoji Liu, Hongwei Jin
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Scattering and Backscattering Study of Mechanical Plane Wave in Composite Materials Plates (Earth model 1066B and LiNbO3) [PDF]
Journal of Applied and Computational Mechanics, 2022 Reflection and refraction phenomenon pattern of elastic plane wave at the interface between anisotropic monoclinic elastic half-space and isotropic elastic half-spaces is studied. Closed-form expression for phase velocity is obtained.
Abhinav Singhal +3 more
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Cramer's rule for implicit linear differential equations over a non-Archimedean ring
Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2022 We consider a linear nonhomogeneous $m$-th order differential equation in a ring of formal power series with coefficients from some field of characteristic zero.
A. Goncharuk
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Solution of System of Symbolic 2-Plithogenic Linear Equations using Cramer's Rule [PDF]
Neutrosophic Sets and Systems, 2023 In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer’s rule was applied to solve the system of symbolic 2-plithogenic linear equations.
P. Prabakaran, Florentin Smarandache
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The core inverse and constrained matrix approximation problem
Open Mathematics, 2020 In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse:||Mx−b||F=minsubjecttox∈ℛ(M),||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in ...
Wang Hongxing, Zhang Xiaoyan
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The explicit formula for Gauss-Jordan elimination applied to flexible systems
Special Matrices, 2022 Flexible systems are obtained from systems of linear equations by adding to the elements of the coefficient matrix and the right-hand side scalar neutrices, which are convex groups of (non-standard) real numbers.
Tran Nam Van +2 more
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Multiparameter Inversion: Cramer's Rule for Pseudodifferential Operators
International Journal of Geophysics, 2011 Linearized multiparameter inversion is a model-driven variant of amplitude-versus-offset analysis, which seeks to separately account for the influences of several model parameters on the seismic response.
Rami Nammour, William W. Symes
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