I am reading through David Widder's Advanced Calculus and he abbreviates a determinant(adsbygoogle = window.adsbygoogle || []).push({});

as:

[tex]

\left( \begin{array}{cccc}

r_{1} \ s_{1} \ t_{1}\\

r_{2} \ s_{2} \ t_{2}\\

r_{3} \ s_{3} \ t_{3}\\

\end{array} \right)

[/tex]

And refers to it by (rst). He then states that expanding by the minors of a given

column, we have:

[tex]

(rst) = r \cdot (s \times t) = s \cdot (t \times r) = t \cdot (r \times s)

[/tex]

Now, I worked it out by looking at the cofactors of r_1, r_2, and r_3 which are the components of the vector (s x t) and confirmed it holds. But how can I see

this property without having to do that? Is there another way to see this say algebraically or geometrically? Some more intuitive way, perhaps?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Determinant, dot product, and cross product

**Physics Forums | Science Articles, Homework Help, Discussion**