Determinant 2

Cofactor

For the cofactor of is where is the matrix obtained from A by deleting the row and the column of A

Lemma

Fix if then

$ε$ Case I: only those survive where these can be thought of a permutation of as permutation of
Sign of and m is the same as is fixed hence $ε$

Case II We can intr change the row and n- columns to bring to the th position.

Theorem

Let A be a matrix and

write out the kth row os A as and all other rows remain the same

Example let

then the Let be distinct (::todo)

Exercise

Show that a unique polynomial of deg that takes arbitrary prescribed value at points

let

as the matrix is invertible being distinct a unique solution

BMath. Notes