[Solved] MATH307 Individual Homework22

Read textbook pages 135 to 142, pages 126 to 128 before working on the homework problems. Show all steps to get full credits.

1. Let A be a square matrix with singular value decomposition A = UV^T, prove that A is invertible if and only if all the singular values of A are nonzero.
2. 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