## MATHS

Class 12th Maths is a very important subject for commerce, science students. Students prefer maths subjects to pursue their dream of becoming engineer, software engineer, technicians. The syllabus will help to gain conceptual understanding of basic concepts and principles applied in day to day work. It will help you to excel with problem solving skills and process the right solutions.

## Reduced Syllabus For CBSE 12 th 2020-2021

Students should download the complete syllabus and ignore reduced syllabus from the list and save time and efforts.The ideal way of doing it is marking the reduced syllabus boldly in your NCERT books and notes and skip those chapters while preparing for exams

The year 2020 has been challenging both for teachers and students. To overcome the spread of pandemic Covid-19 disease, the school and colleges have been providing online classes to all their students. Students continually struggled with low internet speed, power cuts and unnecessary distraction while relay of online classes. This ultimately resulted in chaos and left students incompetent and unprepared. This is where Vidyasetu comes in.

We are a free online library for Class XII students. We provide the updated class 12 thMaths syllabus, Maths books, maths question paper blueprint, Maths marking scheme, Mathspractise manuals, exemplar problems all at one place. We are first to provide the updated study material to our readers.

In the 21st learning era, where conceptual understanding is a must, we provide free video classes on youtube by the best faculties. These classes explain each chapter of maths in such a manner that the students develop a deep understanding about every single topic in the coming syllabus of maths.

### Detailed Marking Scheme for Maths Syllabus 2021

The detailed marking scheme of Maths subject is provided here. The CBSE has deleted some topics from the syllabus for 2021. Students should avoid those deleted topics and primarily focus on high weightage chapters

Units | ChaptersWise | Marks |

Part A | ||

Relations and Functions | Chapter 1-2 of Book 1 | 08 |

Algebra | Chapter 3-4 Of Book 1 | 10 |

Calculus | Chapter 5-6 Of Book 1 | 35 |

Vectors and Three – Dimensional Geometry | Chapter 10-11 Of Book 2 | 14 |

Linear Programming | Chapter 12 Of Book 2 | 05 |

Probability | Chapter 13 Of Book 2 | 08 |

Periodic Tests ( Best 2 out of 3 tests conducted) | 10 | |

Mathematics Activities | For all chapters | 10 |

Total marks | 100 marks |

In this Blog, we will understand the ncert solution and explanation of Matrices or Matrix Class 12 Chapter-3 of MathsNcert book. After understanding the entire chapter you will be able to get the solution for the following questions.

### NCERT Solutions to The Problems

Miscellaneous Exercise on Chapter 3 |

In this video, we will discuss Class 12 Chapter 3 Matrices Exercise-3 Q1 & Q2

Let’s Solve Matrices Chapter 3 Class 12th Maths Exercise 3.2 Question 3.

In this video, we will discuss Class 12 Maths Chapter 3 Exercise 3.2 Q4 & Q5.

In this video, we will discuss the Class 12 Maths Chapter 3 Exercise-3.2 Q6 & Q7 to Q15

### CBSE/NCERT Class 12 Maths Chapter 3, Matrices/Matrix, Lecture-1

The knowledge of matrices is necessary for various branches of mathematics. Matrices are one of the most powerful tools in mathematics. This mathematical tool simplifies our work to a great extent when compared with other straight forward methods.

The evolution of the concept of matrices is the result of an attempt to obtain compact and simple methods of solving a system of linear equations. Matrices are not only used as a representation of the coefficients in a system of linear equations, but the utility of matrices far exceeds that use.

Matrix notation and operations are used in electronic spreadsheet programs for personal computers, which in turn is used in different areas of business and science like budgeting, sales projection, cost estimation, analysing the results of an experiment etc. Also, many physical operations such as magnification, rotation and reflection through a plane can be represented mathematically by matrices. Matrices are also used in cryptography.

This mathematical tool is not only used in certain branches of sciences, but also in genetics, economics, sociology, modern psychology and industrial management. In this chapter, we shall find it interesting to become acquainted with the fundamentals of matrix and matrix algebra.

For a proper introduction of chapter go through our first video lecture in matrix.

### CBSE/NCERT Class 12 Maths Chapter 3, Matrices: Operations on Matrices, Lecture-10

3.4 Operations on Matrices

In this section, we shall introduce certain operations on matrices, namely, the addition of matrices, multiplication of a matrix by a scalar, difference and multiplication of matrices.

3.4.1 Addition of matrices

Suppose Fatima has two factories at places A and B. Each factory produces sports shoes for boys and girls in three different price categories labelled 1, 2 and 3.

For more understanding on operation on matrices watch the online video lecture

### CBSE/NCERT Class 12 Maths Chapter 3, Matrices: Properties of Matrix Addition, Lecture-11

The addition of matrices satisfy the following properties:

(i) Commutative Law If A = [aij], B = [bij] are matrices of the same order, say

m × n, then A + B = B + A.

Now A + B = [aij] + [bij] = [aij + bij]

= [bij + aij] (addition of numbers is commutative)

= ([bij] + [aij]) = B + A

(ii) Associative Law For any three matrices A = [aij], B = [bij], C = [cij] of the

same order, say m × n, (A + B) + C = A + (B + C).

Now (A + B) + C = ([aij] + [bij]) + [cij]

= [aij + bij] + [cij] = [(aij + bij) + cij]

= [aij + (bij + cij)] (Why?)

= [aij] + [(bij + cij)] = [aij] + ([bij] + [cij]) = A + (B + C)

(iii) Existence of additive identity Let A = [aij] be an m × n matrix and

O be an m × n zero matrix, then A + O = O + A = A. In other words, O is the

additive identity for matrix addition.

(iv) The existence of additive inverse Let A = [aij]

m × n be any matrix, then we have another matrix as – A = [– aij] m × n

such that A + (– A) = (– A) + A= O. So – A is the additive inverse of A or negative of A.

Find solutions on properties of Matrix addition and watch our online video lectures.

### CBSE/NCERT Class 12 Maths Chapter 3, Matrices: Properties of Matrix Multiplication by Scalar, Lec-12

If A = [aij] and B = [bij] be two matrices of the same order, say m × n, and k and l are

scalars, then

(i) k(A +B) = k A + kB, (ii) (k + l)A = k A + l A

(ii) k (A + B) = k ([aij] + [bij])

= k [aij + bij] = [k (aij + bij)] = [(k aij) + (k bij)]

= [k aij] + [k bij] = k [aij] + k [bij] = kA + kB

(iii) ( k + l) A = (k + l) [aij]

= [(k + l) aij] + [k aij] + [l aij] = k [aij] + l [aij] = k A + l A

Watch this video, you will understand Properties of scalar multiplication of a matrix.

### CBSE/NCERT Class 12 Maths Chapter 3, Matrices: Matrix Multiplication, Lecture-13

The main condition of matrix multiplication is that the number of columns of the 1st matrix must equal the number of rows of the 2nd one.

Learn more from our video lectures in Matrix multiplication.

### CBSE/NCERT Class 12 Maths Chapter 3, Matrices: Matrix Multiplication, Lecture-14

In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices {\displaystyleA}A and {\displaystyle B}B is then denoted simply as {\displaystyle AB}AB.[1][2]

Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812,[3] to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering.[4][5] Computing matrix products is a central operation in all computational applications of linear algebra.

Still finding it difficult!, Watch the full video to have clear understanding

### CBSE/NCERT Class 12 Maths Chapter 3, Matrices: Properties of Matrix Multiplication, Lecture-15

The multiplication of matrices possesses the following properties, which we state without proof.

1. The associative law For any three matrices A, B and C. We have

(AB) C = A (BC), whenever both sides of the equality are defined.

2. The distributive law For three matrices A, B and C.

(i) A (B+C) = AB + AC

(ii) (A+B) C = AC + BC, whenever both sides of equality are defined.

3. The existence of multiplicative identity For every square matrix A, there

exist an identity matrix of the same order such that IA = AI = A.

Watch the video to clear the concept.

### CBSE/NCERT Class 12 Maths Chapter 3, Matrices: Difference of Two Matrix, Lecture-16

Mark the difference between two matrices through a procedure. Watch the video to know what the differences are.

### CBSE/NCERT Class 12 Maths Chapter 3, Matrices: Transpose of Matrix & its Properties, Lecture-17

3.5.1 Properties of the transpose of the matrices

We now state the following properties of the transpose of matrices without proof. These may be verified by taking suitable examples.

For any matrices A and B of suitable orders, we have

(i) (A′)′ = A, (ii) (kA)′ = kA′ (where k is any constant)

(iii) (A + B)′ = A′ + B′ (iv) (A B)′ = B′ A′

Simply the equation with the help of video lecture.

### CBSE/NCERT Class 12 Maths Chapter 3, Matrices: Symmetric & Skew Symmetric Matrix, Lecture-18

Definition 4 A square matrix A = [aij] is said to be symmetric if A′ = A, that is,

[aij] = [aji] for all possible values of i and j.

Get the concept clear with our online lecture on Chapter 3 of class 12th maths

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