I have been solving least squares problems and I came across the following problem:
"Construct an algorithm based on the $QR$ decomposition ($A=QR$) that determines whether a square matrix is singular or not, you explicitly write your algorithm".
What I have tried is to do $QR$ and if it can check the determinant of $R$ and if it is zero the matrix A is singular.
My doubt is if what I am doing makes sense or if on the contrary there is a better way to do it(where some property of $QR$ is applied)?