Answer to Question #148916 in Linear Algebra for Dhruv bartwal

Question

If M is a singular Matrix, is there a value of k∈N for which kM will be non singular? Give reasons for your answer

Answer 1

A square matrix is called singular if its determinant is 0. So, $\det (M)=0$. Taking into account that $\det (kM)=k^n\det (M)$ where $n$ is a number of rows in $M$, we conclude that $\det (kM)=k^n\det (M)=k^n\cdot 0=0$ for all $k\in \mathbb N.$ Therefore, $kM$ is a singular matrix as well.