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 (x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3}) is given **= 1/2[x _{1}(y_{2}–y_{3}) + x_{2}(y_{3}–y_{1}) + x_{3}(y_{1}–y_{2})]**

**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

### 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

–: End of ML Aggarwal Solutions Determinant ISC Class 12 Maths Ch-4 :–

Return to :- ML Aggrawal ISC Class-12 Maths Vol-1 Solutions

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