NCERT Solutions for Class 12 Maths Chapter 4 Determinants

1. Determinant of order one: Consider a matrix A = [a], the determinant of this matrix is equal to a.

2. Determinant of order two: If the order of the matrix is 2, and the given matrix A is-  \([ \begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22}\\ \end{matrix} ]\)
   Determinant of A, |A| = \(| \begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22}\\ \end{matrix} |\), = a₁₁.a₂₂ - a₂₁.a₁₂

3. Determinant of order three:  If the order of the matrix is 2, and the given matrix A is-  \([ \begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\ \end{matrix} ]\)
   Determinant of A, |A| = a₁₁ a₂₂ a₃₃ – a₁₁ a₂₃ a₃₂ – a₁₂ a₂₁ a₃₃ + a₁₂ a₂₃ a₃₁ + a₁₃ a₂₁ a₃₂ – a₁₃ a₃₁ a₂₂

Minor = \(\begin{array}{l}M_{f}=\begin{vmatrix} a & b\\ g & h \end{vmatrix}\end{array}\), M_f = a.h – b.g

Cofactor of an element a_ij in determinant is defined as A_ij= (-1)^i+jM_ij