Cramer's Rule and Matrix Inverse

This lecture covers Cramer's Rule for solving systems of linear equations using determinants, including the unique solution of the equation Ax=b. It also explores the formula for calculating the matrix inverse and the application of Cramer's Rule in determining the dependence of the solution on the vector b. Additionally, it delves into the concept of cofactor matrices and the adjoint matrix. The lecture concludes with a discussion on the volume of parallelepipeds and the properties of vector spaces and subspaces.