Visualize the Gaussian algorithm through a 14-minute video that explores its geometric interpretation and application in linear algebra. Delve into the algebraic method of solving systems of linear equations, examining both 2D and 3D operations from geometric and algebraic perspectives. Explore how the algorithm manipulates planes and lines to align with coordinate axes, and discover its role in breaking down linear transformations into simpler components. Gain insights into elementary matrices and their geometric representations, enhancing your understanding of this fundamental concept in linear algebra.