Results 181 to 190 of about 4,548 (226)

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 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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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 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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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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Cramer's rule on 2-by-2 systems

ACM SIGNUM Newsletter, 1974
Cramer's rule expresses the solution to a system of simultaneous linear equaations in terms of ratios of determinants. It is widely known as an example of an impractical method for large systems because of the time required to compute the determinants.
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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 Is Due To Cramer

Mathematics Magazine, 2001
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Cramer's Rule

2001
Saul I. Gass, Carl M. Harris
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