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Another Geometric Interpretation of Cramer’s Rule (Journal Article)

By: Material type: TextTextSeries: Mathematics Magazine ; Volume 96: Number 4, October 2023Publication details: Philadelphia, PA :Taylor & Francis Group , September 2023Description: 455-462pISSN:
  • 0025-570X
Subject(s): Online resources:
Contents:
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Summary: Abstract: We develop a geometric interpretation of Cramer’s rule as a generalization of projection onto orthogonal basis vectors using the rows of the adjugate. This interpretation makes connections between elementary linear algebra concepts like the solution to linear equations, inner products, and projections. Such connections are useful for introducing broader concepts related to Hilbert spaces and geometric algebras like Grassman algebra. Such connections were essential for the author’s mathematical education as an engineer.
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Abstract: We develop a geometric interpretation of Cramer’s rule as a generalization of projection onto orthogonal basis vectors using the rows of the adjugate. This interpretation makes connections between elementary linear algebra concepts like the solution to linear equations, inner products, and projections. Such connections are useful for introducing broader concepts related to Hilbert spaces and geometric algebras like Grassman algebra. Such connections were essential for the author’s mathematical education as an engineer.

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