Matrix/Characteristic polynomial/Homothety/Exercise

Let ${}M$ be an ${}n\times n$-matrix, with the characteristic polynomial

${}\chi _{M}=X^{n}+c_{n-1}X^{n-1}+c_{n-2}X^{n-2}+\cdots +c_{2}X^{2}+c_{1}X+c_{0}\,.$

Determine the characteristic polynomial of the scaled matrix ${}sM$, ${}s\in K$.

Create a solution