Abstract
We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of n-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the original coordinate vector with Dirac delta functions and changing integration variables from the original coordinates to new coordinates. As a byproduct, we derive a generalized version of Cramer's rule that applies to a partial set of variables, which is new to the best of our knowledge. Our formulation of finding a transformation rule for multi-variable functions shall be particularly useful in changing a partial set of generalized coordinates of a mechanical system.
Original language | English |
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Article number | 065002 |
Journal | European Journal of Physics |
Volume | 41 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2020 Nov |
Keywords
- Cramer s rule
- Dirac delta function
- generalized coordinates
ASJC Scopus subject areas
- Physics and Astronomy(all)