Question

How can i do:

Answer 1

\[\det\left[\begin{matrix}1 & 1 & 1 \\ x & y & z \\ x² & y² &z²\end{matrix}\right]\]

Answer 2

How i can think to solve this? Help-me!

Answer 3

Just use the "big formula" mentioned in the lectures. For 3X3 matrices (or smaller), it happens to work out that you add the products along diagonals going down and right and subtract the products along diagonals going down and left, but generally speaking, just multiply every combination of entries without repeated rows or columns.For \[\left[\begin{matrix}a &b &c \\ d & e &f\\ g &h &i \end{matrix}\right]\]
this works out to aei-afh+bfg-bdi+cdh-ceg.

Answer 4

The result is factorable, and if you perform elimination on the matrix the factors will be on the diagonal.