Page 1 - Lesson Notes

Chapter- 4, Determinants

Lesson Notes.

Determinant: Determinant is the numerical value of the square matrix. So, to
every square matrix A = [a ij] of order n, we can associate a number (real or
complex) called determinant of the square matrix A. It is denoted by det A or
|A|.

Note
(i) Read |A| as determinant A not absolute value of A.
(ii) Determinant gives numerical value but matrix do not give numerical value.
(iii) A determinant always has an equal number of rows and columns, i.e. only
square matrix have determinants.

Value of a Determinant

Value of determinant of a matrix of order 2, A = is

Value of determinant of a matrix of order 3, | A | is given by expressing it in
terms of second order determinant. This is known as expansion of a
determinant along a row (or column).

Note
(i) For easier calculations of determinant, we shall expand the determinant
along that row or column which contains the maximum number of zeroes.
(ii) While expanding, instead of multiplying by (−1) + we can multiply by +1 or
-1 according to as (i + j) is even or odd resectively.