Cramer's rule, explained geometrically: Essence of Linear Algebra - Part 12 of 15

The video explores the geometry and application of Cramer's rule for solving linear systems of equations. It discusses the limitations of Cramer's rule compared to Gaussian elimination and delves into the geometric interpretation of coordinates as areas and volumes. The video also covers orthonormal transformations and generalizes these concepts to higher dimensions.

Discuss the role of orthonormal matrices in solving linear systems.

In what ways can the concept of signed areas and volumes be generalized to higher dimensions?

What is the relationship between the determinant of a transformation matrix and the scaling of areas during transformations?

What is the significance of the transformation matrix in determining the output of a linear system?