Exercise 4.2.25

Answers

Applies Theorem 4.3 to each row. Thus we have hat

\det (\begin{matrix} k a_{1} \\ k a_{2} \\ ⋮ \\ k a_{n} \end{matrix}) = k \det (\begin{matrix} a_{1} \\ k a_{2} \\ ⋮ \\ k a_{n} \end{matrix}) = \dots = k^{n} \det (\begin{matrix} a_{1} \\ a_{2} \\ ⋮ \\ a_{n} \end{matrix}) .

jephianlin

2011-06-27 00:00