Determinant ISC Class 12 Maths ML Aggarwal Solutions

Determinant ISC Class 12 Maths ML Aggarwal Solutions Ch-4. Step by step Solutions of ML Aggarwal ISC Class-12 Mathematics with all exercise and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

ML Aggarwal Solutions of Determinant Questions for ISC Class 12 Mathematics

Board	ISC
Class	12
Subject	Mathematics
Chapter-4	Determinant
Session	2024-25
Topics	Solutions of ML Aggarwal

Determinant

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

Determinant of the order one (1×1)

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

Properties of 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 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

Area of Triangle Using Determinant

area of a triangle whose vertices are (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given = 1/2[x₁(y₂–y₃) + x₂(y₃–y₁) + x₃(y₁–y₂)]

Singular and non-singular Matrix

If the value of determinant corresponding to a square matrix is zero, then the matrix is said to be a singular matrix, otherwise it is non-singular matrix, i.e. for a square matrix A, if |A| ≠ 0, then it is said to be a non-singular matrix and of |A| = 0, then it is said to be a singular matrix.

Adjoint of a Matrix

The adjoint of a square matrix ‘A’ is the transpose of the matrix which obtained by cofactors of each element of a determinant corresponding to that given matrix. It is denoted by adj(A).
In general, adjoint of a matrix A = [a