Determinants — Chapter Summary

A determinant is a number associated

A determinant is a number associated with every square matrix A = [aij] of order n. It is denoted by |A|, det A, or Δ. It is not the same as modulus.

For a 1 × 1 matrix

For a 1 × 1 matrix A = [a11], the determinant is |a11| = a11.

For A = [a11 a12

For A = [a11 a12; a21 a22], the determinant is |A| = a11a22 - a12a21.

For a 3 × 3 matrix

For a 3 × 3 matrix, expansion along the first row gives |A| = a11a22a33 - a11a32a23 - a12a21a33 + a12a31a23 + a13a21a32 - a13a31a22. The same value is

For easier calculation

For easier calculation, the determinant is expanded along the row or column containing the maximum number of zeros.