1
$\begingroup$

Suppose $k<n$. How does one express $\det\begin{pmatrix}a_1^1&\dots&a_n^1\\ \vdots&\ddots&\vdots\\ a^n_1&\dots&a^n_n\end{pmatrix}$ in terms of a linear combination of determinants $\det\begin{pmatrix} a_1^{i_1}&\dots&a_k^{i_1}\\ \vdots&\ddots&\vdots\\ a^{i_k}_1&\dots&a^{i_k}_k\end{pmatrix},$ where $1\leq i_1<i_2<i_3<\cdots<i_k\leq n$?

$\endgroup$
1
$\begingroup$

Just develop according to the last column $(n-k)$ times.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.