Plus Two Maths Notes Chapter 4 Determinants is part of Plus Two Maths Notes. Here we have given Plus Two Maths Notes Chapter 4 Determinants.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus Two |

Subject | Maths Notes |

Chapter | Chapter 4 |

Chapter Name | Determinants |

Category | Kerala Plus Two |

## Kerala Plus Two Maths Notes Chapter 4 Determinants

**Some Properties of Determinants**

- Determinant I
_{n}= I (I_{n}– identity matrix of order n) - If A and B are square matrices of the same order |AB| = |A| |B|
- If A is a square matrix of order n and λ is any scalar. |λ A| = λ
^{n }|A| - If A is a non-singular matrix of order n, then |(adj A)| = |A|
^{n-1} - |A| = |A
^{T}| - |A
^{n}| = |A|^{n}if n is a positive integer. - The value of a determinant will not be changed.
- if the rows and columns are interchanged.
- lf one row or column is multiplied by a conštant and added to another row or column.
- The value of the determinant is zero if
- Two rows (column) are identical
- Two rows (column) are proportional
- If a row (column) of a determinant is multiplied by a constant, the value of the determinänt becomes that constant times the original value.
- . If the elements of a row (column) of a determinant are the sum of two numbers then the determinant is the sum of two determinants as follows:

- If elements of a row or column are multiplied with co-factors of any other row or column then their sum is zero. For eg: a
_{11}A_{21}+ a_{12}A_{22}+ a_{13}A_{23}= 0 - Consider the system of equations

a_{1}x + b_{1}y + c_{1}z = d_{1}

a_{2}x + b_{2}y + c_{2}z = d_{2}

a_{3}x + b_{3}y + c_{3}z d_{3}To solve this system of equations using the matrix method,

The above system of equations can be expressed as AX = B, then the solution is given by X = A^{-1}B.

(i) 1f |A| ≠ 0 the system is consistent and has a unique solution given by X = A^{-1}B

(ii) If |A| = 0 and (adjA)B ≠ 0, the system is inconsistent and has no solution.

(iii) If |A| = 0 and (adj)B = 0, then the sys. tern may be consistent and has infinitely many solutions. In order to find these infinitely many solutions, replace one of the variables by k (say z = k) and solve any two of the given equations for x and y ¡n terms of k. - Area of a triangle with vertices

We hope the Kerala Plus Two Maths Notes Chapter 4 Determinants help you. If you have any query regarding Kerala Plus Two Maths Notes Chapter 4 Determinants, drop a comment below and we will get back to you at the earliest.