Results 211 to 220 of about 2,174,992 (257)

Another Geometric Interpretation of Cramer’s Rule

Mathematics Magazine, 2023
Summary We develop a geometric interpretation of Cramer’s rule as a generalization of projection onto orthogonal basis vectors using the rows of the adjugate.
Benjamin W. L. Margolis
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Cramer’s rule for a system of quaternion matrix equations with applications

Applied Mathematics and Computation, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guang-Jing Song   +2 more
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106.04 A geometric interpretation of Cramer’s rule

The Mathematical Gazette, 2022
When is invertible, this scheme works very well. As , the dimension of the solution set is . We are left to find the direction perpendicular to all the rows of . A rank [A, −b] = rank A = n (n + 1) − n = 1 [A, −b] Exterior product will do the job.
Hailiang Hu
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New approach to the generalized cross product. Orthonormal sets and Cramer's rule

International Journal of Algebra, 2023
In this work we develop the generalized cross product, in a different way from what has been reported in several research ...
E. Salinas-Hernández   +2 more
semanticscholar   +1 more source

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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