Results 211 to 220 of about 872 (250)

Layer-Specific Astrocyte Morphological Responses in the CA3 Hippocampus Region During Piry Virus-Induced Encephalitis. [PDF]

open access: yesHippocampus
de Almeida Miranda D   +10 more
europepmc   +1 more source

An Alternate Proof of Cramer's Rule

open access: yesThe 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.
Stephen H. Friedberg
openaire   +2 more sources

A Geometrical Approach to Cramer's Rule

open access: yesMathematics Magazine, 1989
(1989). A Geometrical Approach to Cramer's Rule. Mathematics Magazine: Vol. 62, No. 1, pp. 35-37.
J. W. Orr
openaire   +2 more sources

A Nonstandard Approach to Cramer's Rule

open access: yesThe 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
Sidney H. Kung
openaire   +2 more sources

A Conceptual Proof of Cramer's Rule

open access: yesMathematics 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.
Richard Ehrenborg
openaire   +2 more sources

Cramer's rule in the Zariski topos

open access: yes, 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.
Gonzalo E. Reyes
openaire   +2 more sources

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