Read textbook pages 135 to 142, pages 126 to 128 before working on the homework problems. Show all steps to get full credits.
- Let A be a square matrix with singular value decomposition A = UΣVT, prove that A is invertible if and only if all the singular values of A are nonzero.
- Prove that the determinant of a square matrix is equal to the product of all its eigenvalues.
Use the result of the previous problem to prove that a square matrix is invertible if and only if its determinant is nonzero
