Determinant Formulas and Cofactors

June 6, 2019

Formula for Determinant

The lecture explains it clearly

Cofactors

Cofactor of $a_{ij}$ is $c_{ij}=\pm *\det(n-1\ matrix\ with\ row\ i\ col\ j\ removed)$ and is +1 when $i+j$ is even and -1 when it is odd. $c_{ij}$ is the cofactor.With cofactor, we can write the formula for determinant “more” concisely $\det A=a_{11}c_{11}+...a_{1n}c_{1n}$ This in fact is not constrained to row 1, it can happen to any rows in the matrix, $\det A=a_{i1}c_{i1}+...+a_{in}c_{in}$