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A New Insight into Cramer’s Rule via the Determinants of Block Matrices

The College Mathematics Journal
Summary This note is to study the connection between Cramer’s rule and the determinants of block matrices, which aims at finding a new proof of Cramer’s rule.
Shaowu Huang
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A Short Proof of Cramer's Rule

Mathematics Magazine, 1970
S. M. Robinson
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Cramer’s rule over quaternions and split quaternions: A unified algebraic approach in quaternionic and split quaternionic mechanics

, 2020
This paper aims to present, in a unified manner, Cramer’s rule which are valid on both the algebras of quaternions and split quaternions.
Gang Wang, Dong Zhang, Zhenwei Guo, T. Jiang   +3 more
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A Generalization of Cramer's Rule

The Two-Year College Mathematics Journal, 1983
(1983). A Generalization of Cramer's Rule. The Two-Year College Mathematics Journal: Vol. 14, No. 3, pp. 203-205.
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Thevenin?s Theorem, Cramer's Rule, and Parameterized Systems: Some Connections [Lecture Notes]

IEEE Control Systems, 2019
Engineering systems are complex systems comprising interconnections of simpler subsystems. Examples of this in electrical engineering are ac and dc circuits, motor drives, power systems, and electronic circuits.
Shankar P. Battacharyya, V. Oliveira, Rafael F.Q. Quirino   +2 more
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Solving constrained matrix equations and Cramer rule

Applied Mathematics and Computation, 2004
The authors consider the matrix equation \(AXB=D\) where the matrices with complex entries \(A\), \(B\), \(D\) are respectively \(m\times n\), \(p\times q\), \(m\times q\), under the constraints \(R(X)\subseteq T\), \(N(X)\supseteq \widetilde{S}\) for the predetermined subspaces \(T\subseteq {\mathbb C}^n (\dim T\leq \operatorname{rank} A ...
Guorong Wang, Sanzheng Qiao
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An Alternate Proof of Cramer's Rule

The College Mathematics Journal, 1988
In almost every introductory book on linear algebra, the proof of Cramer's Rule assumes that students are familiar with the classical adjoint, adjyl, of a matrix A. The proof then uses the result that ^4(adj A) = (det^l)J. In their text Matrix Analysis [Cambridge University Press, New York, 1985, p. 21], Roger A. Horn and Charles A.
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Condensed cramer rule for solving restricted matrix equations

Applied Mathematics and Computation, 2006
A Cramer rule for solving restricted matrix equations of the kind \(WAWX\widetilde{W} B\widetilde{W}=D\), \(R(X)\subset R[(AW)^{k_1}]\), \(N(X)\supset N[(\tilde{W}B)^{k_2}]\) was presented by \textit{G. Wang} and \textit{J. Sun} [Appl. Math. Comput. 154, 415--422 (2004; Zbl 1055.15024)].
Chao Gu, Guorong Wang
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A Geometrical Approach to Cramer's Rule

Mathematics Magazine, 1989
(1989). A Geometrical Approach to Cramer's Rule. Mathematics Magazine: Vol. 62, No. 1, pp. 35-37.
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A Nonstandard Approach to Cramer's Rule

The College Mathematics Journal, 1988
Sidney H. Kung, Jacksonville, FL Most textbooks in linear algebra develop Cramer's rule via the adjoint matrix. Therefore, the following approach may be worth noting. Cramer'_ rule. If the coefficient matrix A of the system + *_,.*,. = *i ^ir*_ ' a\2x2 ' a2-\X-\ i a22x2 i a) a?iX1 + an2x2 + ??? +annxn = b? has nonzero determinant, then the system has a
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