Results 121 to 130 of about 4,516 (175)

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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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)].
Gu, Chao, Wang, Guorong
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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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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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A Conceptual Proof of Cramer's Rule

Mathematics Magazine, 2004
Proof. The classical way to solve a linear equation system is by performing row operations: (i) add one row to another row, (ii) multiply a row with a nonzero scalar and (iii) exchange two rows. We show that the quotient in equation (1) will not change under row operations.
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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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Cramer's rule reconsidered or equilibration desirable

ACM SIGNUM Newsletter, 1980
Consider the solution of systems of two linear equations, for which Cramer's rule has some attractions [3]. It is claimed by Moler [3] that Cramer's rule is of unsatisfactory accuracy even in this case, whereas the claim is made that Gaussian eliminatino with pivoting is good (a related analysis, cited by Moler, is that of Bauer [1]).
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Cramer’s Rules for Some Hermitian Coquaternionic Matrix Equations

Advances in Applied Clifford Algebras, 2017
The author uses row-column determinants that he had introduced in some earlier work to investigate properties of the determinant of a Hermitian matrix, and to give determinantal representations of the inverse of a Hermitian coquaternionic matrix.
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Cramer's rule in the Zariski topos

1979
This note is a remark on Kock's work on linear algebra in the Zariski topos [2] . We point out that his main result implies a version of Cramer's rule for the generic local A-algebra in the Zariski topos Z/Spec(A) . A constructive version of the Jacobian criterion for unramified morphisms of [4] is obtained as a consequence.
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Cramer's Rule

2001
Saul I. Gass, Carl M. Harris
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