### myCBSEguide App

Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Install Now**Matrices Class 12 Notes Mathematics** in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Matrices class 12 Notes latest chapter wise notes for quick preparation of CBSE board exams and school-based annual examinations. Class 12 Mathematics notes on chapter 3 Matrices are also available for download in CBSE Guide website.

## Matrices Class 12 Notes Mathematics

Download CBSE class 12th revision notes for chapter 3 Matrices in PDF format for free. Download revision notes for Matrices class 12 Notes and score high in exams. These are the Matrices class 12 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter 3 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days.

**Download Revision Notes as PDF**

**CSBE Class 12 Mathematics Chapter 3 Matrices**

- A
**matrix**is an ordered rectangular array of numbers, real or complex or functions. - A matrix having m rows and n columns is called a matrix of
**order**m × n. **Column matrix**: A matrix with one column is denoted by .**Row matrix**: A matrix with one row is denoted by .**Square matrix**: An m × n matrix is a square matrix if m = n.**Diagonal matrix**: A = is a diagonal matrix if =0, when**Scalar matrix**: is a scalar matrix if when i ≠ j, (k is*some constant), when I=j.***Identity matrix**: is an identity matrix, if**Zero matrix**: A zero matrix has all its elements as zero.**Equality of two matrices**: if (i) A and B are of same order, (ii) for all possible values of**Scalar multiplication**:

Also – A = (–1)A

- A – B = A + (–1) B

A + B = B + A

(A + B) + C = A + (B + C), where A =

B = and C = are of same order.- k(A + B) = kA + kB, where A and B are of same order, k is constant.
- (k + l ) A = kA + lA, where k and l are constant.
- where

- (i) A(BC) = (AB)C,

(ii) A(B + C) = AB + AC,

(iii) (A + B)C = AC + BC

- (i) (A′)′ = A, · (ii) (kA)′ = kA′, · (iii) (A + B)′ = A′ + B′, · (iv) (AB)′ = B′A′
**Symmetric matrix**: A is a symmetric matrix if A′ = A.**Skew-aymmetric matrix**: A is a skew symmetric matrix if A′ = –A.- Any square matrix can be represented as the sum of a symmetric and a skew symmetric matrix. In fact, A = (A + A’) + (A – A’), where (A + A’) is a symmetric matrix and (A – A’) is a skew-symmetric matrix.
**Equivalent matrices**: Two matrices A and B are equivalent that is, A – B is A is obtained from the other by a sequence of elementary operations. Elementary operations of a matrix are as follows:

(i)

or (interchange rows or columns)(ii)

or(iii)

or- If A and B are two square matrices such that AB = BA = I, then B is the inverse matrix of A and is denoted by and A is the inverse of B.
- Inverse of a square matrix, if it exists, is unique.

**CBSE Class 12 Revision Notes and Key Points**

Matrices class 12 Notes Mathematics. CBSE quick revision note for class-12 Chemistry Physics Math’s, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

- Physics
- Chemistry
- Mathematics
- Biology
- Accountancy
- Economics
- Business Studies
- Computer Science
- Informatics Practices
- English Core
- History
- Physical Education

To download Matrices class 12 Notes Mathematics, sample paper for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT Matrices, NCERT Exemplar Matrices, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through **the best app for CBSE students** and myCBSEguide website.

- Relations and Functions class 12 Notes Mathematics
- Inverse Trigonometric Functions class 12 Notes Mathematics
- Determinants class 12 Notes Mathematics
- Continuity and Differentiability class 12 Notes Mathematics
- Application of Derivatives class 12 Notes Mathematics
- Integrals class 12 Notes Mathematics
- Application of Integrals class 12 Notes Mathematics
- Differential Equations class 12 Notes Mathematics
- Vector Algebra class 12 Notes Mathematics
- Three Dimensional Geometry class 12 Notes Mathematics
- Linear Programming class 12 Notes Mathematics
- Probability class 12 Notes Mathematics

### Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

Create Now### myCBSEguide

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

Install Now