chapter  5
17 Pages

Determinants

ByQingwen Hu

We know that the 2 × 2 matrix A = a b c d $ A = \left[ {\begin{array}{*{20}l} a \hfill & b \hfill \\ c \hfill & d \hfill \\ \end{array} } \right] $ is invertible if and only if the scalar ad| - bc ≠ 0. And we also learned that elementary row operations do not change invertibility of a matrix. If we regard the scalar ad bc $ \text{ad}\text{bc} $ as the value of a function, called determinant det $ {\text{det }} $ acting on the matrix A, we wish to know how elementary row operations will change the function value.