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.

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

Exe-4.1

Determinant ISC Class 12 Maths ML Aggarwal Solutions Ch-4

Exe-4.2

Determinant ISC Class 12 Maths ML Aggarwal Solutions Ch-4

Exe-4.3

Determinant ISC Class 12 Maths ML Aggarwal Solutions Ch-4

Exe-4.4

Determinant ISC Class 12 Maths ML Aggarwal Solutions Ch-4

Exe-4.5

Determinant ISC Class 12 Maths ML Aggarwal Solutions Ch-4

Exe-4.6

Determinant ISC Class 12 Maths ML Aggarwal Solutions Ch-4

Exe-4.7

Determinant ISC Class 12 Maths ML Aggarwal Solutions Ch-4

Ch-Test

Determinant ISC Class 12 Maths ML Aggarwal Solutions Ch-4

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