# Tagged Questions

Laplace expansion is a method for expanding determinants in terms of minors, determinants of some related smaller matrices.

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### Is there a simple way of calculating determiant of “reverse arrowhead” matrix?

I have some problems with finding determinant of the following matix. It seems easy but I keep getting something wrong. I have tried simple Laplace expansion on the first row, but I have a feeling I ...
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### Proof of Leibniz formula from Laplace expansion

I'm trying to prove Leibniz formula for the determinant using Laplace expansion. Here's my attempt: For a $1 \times 1$ matrix $A = \begin{pmatrix}a_{11}\end{pmatrix}$, define $\det A = a_{11}$. For ...
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### What seems to be the minors of the Adjugate matrix $\text{adj}(A)$ of a square matrix $A$?

It is by definition that entries of the adjugate matrix $\text{adj}(A)$ are the corresponding $(n-1)$-minors of $A$ (up to a sign). What can we say about the $k$-minor of $\text{adj}(A)$ in relation ...
### What is the 3-volume of the 3-parallelepiped defined by $\left\{\vec{v_1},\vec{v_2},\vec{v_3}\right\}$?
We have $\left\{\vec{v_1},\vec{v_2},\vec{v_3}\right\}=\left\{\begin{bmatrix}1\\0\\0\\0\end{bmatrix},\begin{bmatrix}1\\1\\1\\1\end{bmatrix},\begin{bmatrix}1\\2\\3\\4\end{bmatrix}\right\}$ QR-...