Determinants For Class 12

Every square matrix A of the order n, can associate a number called determinants of the square matrix A.

Determinant of the order 1×1-

Consider a matrix A = [a], then the determinant of the matrix is equal to a.

Determinant of the order 2×2-

If the order of the matrix is 2, then the determinants is defined matrix A, where A is-

\(A= \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22} \end{bmatrix}\)

Determinant of A = \(\left |A \right |= \begin{vmatrix} a_{11} & a_{12}\\ a_{21} & a_{22} \end{vmatrix}\)

\(= a_{11}. a_{22} – a_{21}.a_{12}\)

Similarly we can find the determinant of the order 3×3

Let us now look on to the properties of the Determinants:

Property 1- The value of the determinant remains unchanged if the rows and columns of a determinant are interchanged.

Property 2- If any two rows (or columns) of a determinants are interchanged, then sign of determinants changes.

Property 3- If any two rows or columns of a determinant are equal or identical, then the value of the determinant is 0.

Property 4- If each element of a row or a column is multiplied by a constant value k, then the value of the determinant originally obtained is multiplied with k.

Determinants for Class 12
Determinants for Class 12
Determinants for Class 12


Practise This Question

The least positive integer n which will reduce (i1i+1)nto a real number , is