March 3, 2022

The Central Board of Secondary Education had developed a new elective course for the class 12 Commerce stream i.e. Applied Maths. Algebra is considered one of the main topics of applied maths in class 12.

In the CBSE Class 12 Board Exam, Algebra covers 10 marks out of 80 marks. This post takes you through detailed information about CBSE Class 12 Applied Maths Algebra.

As per the **CBSE Class 12 Applied Maths Syllabus** the main topics that you will be studying in Algebra are:

**Matrices:**In matrices, you will study the types of matrices, zero and identity matrices, transpose of a matrix, symmetric and skew-symmetric matrices, operation on matrices, simple properties of addition, multiplication, and scalar multiplication, the concept of elementary row and column operations, and etc.**Determinants:**In determinants, you will be studying the determinant of a square matrix (3x3 matrices), properties of determinants, minors, cofactors, and application of determinants in finding the area of a triangle, Adjoint and inverse of a square matrix, consistency, inconsistency, and the number of solutions of the system of linear equation by examples, and etc.- Cramer’s rule and its application.
- Simple applications of matrices and determinants including Leontief input-output model for two variables.

Read About **CBSE Class 12 Applied Maths Probability**

- You will get the best and easy understandable notes of Applied maths Algebra from the link provided in this article.
- The notes will include important CBSE Class 12 Algebra Questions.
- You will be getting the notes in both English as well as the Hindi Language. It is beneficial for you to study and understand the concept easily.
- The algebra topic holds a weightage of 13 marks in applied maths of class 12.
- The notes provided on this page have been made by experts and highly experienced teachers. The notes are made in simple language.
- You can download the CBSE class 12 Applied maths Algebra notes PDF by just clicking on the link provided on this page.

Read About **CBSE Class 12 Applied Maths Basic Financial with Mathematics**

You will be studying various topics in the Applied maths Algebra section that are Matrices, Determinants, Cramer’s rule and its application, and Simple applications of matrices and determinants including Leontief input-output model for two variables.

Knowing the syllabus will help you know important Applied Maths Algebra CBSE class 12 topics and focus more on those topics to score good marks in the exam. The table below shows the CBSE class 12 Applied Maths Algebra syllabus 2021:

Topics |
Explanation of Topics |

Matrices |
Concept of matrices, Notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication, and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (restricted to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). |

Determinants |
Concept of Determinant, Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors, and applications of determinants in finding the area of a triangle Adjoint and inverse of a square matrix Consistency, inconsistency, and number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using an inverse of a matrix |

Cramer’s rule and its Application |
Concept of Cramer’s rule and its Application, Derivation of application. |

Simple applications of matrices and determinants including Leontiff input-output model for two variables |
Concept of Simple applications of matrices and determinants including Leontiff input-output model for two variables. |

**Read about: ****CBSE Class 12 Linear programming**

To help you better understand the type of questions asked from the algebra topic, we have provided few sample questions here.

**Question 1: **Under what conditions on the real numbers a, b, c, d, e, f do the simultaneous equations ax + by = e and cx + dy = f have (a) a unique solution, (b) no solution, (c) infinitely many solutions in x and y. Select values of a, b, c, d, e, f for each of these cases, and sketch on separate axes the lines ax+by = e and cx+dy = f.

**Question 2:** For what values of a do the simultaneous equations x + 2y + a2z = 0, x + ay + z = 0, x + ay + a2z = 0 have a solution other than x = y = z = 0. For each such a find the general solution of the above equations.

**Question 3: **Do 2 × 2 matrices exist satisfying the following properties? Either find such matrices or show that no such exist.

- (i) A such that A5 = I and Ai 6= I for 1 ≤ i ≤ 4
- (ii) A such that An 6= I for all positive integers n
- (iii) A and B such that AB 6= BA
- (iv) A and B such that AB is invertible and BA is singular (i.e. not invertible)
- (v) A such that A5 = I and A11 = 0

**Question 4: ** (a) Find the remainder when n2 + 4 is divided by 7 for 0 ≤ n < 7. Deduce that n2 + 4 is not divisible by 7, for every positive integer n. [Hint: write n = 7k + r where 0 ≤ r < 7.] (b) Now k is an integer such that n3 + k is not divisible by 4 for all integers n. What are the possible values of k?

Read About **CBSE Class 12 Applied Maths Inferential Statistics**

Frequently Asked Questions

What is the weightage of Algebra section in Applied maths subject of class 12?

The Algebra section holds a weightage of 13 marks in Applied Maths subject of class 12.

What are the topics which will be taught in Applied Maths Algebra section class 12?

The topics which will be taught in Applied maths Algebra section class 12 are: -

- Matrices
- Determinants
- Cramer’s Rule and its Application
- Simple Applications of Matrices and Determinants including Leontiff input-output model for two variables.

What are the best reference books for the CBSE class 12 Applied Maths Subject?

The best reference books are: -

- Applied Mathematics for Class 12 (set of 2 Volume) by R.D. Sharma.
- Elements of Mathematics for Class XII (Vol - I & Vol –II) by M.L. Bhargava, Janardan Dinodia.
- A textbook of Applied Mathematics for Class 12 (Vol. 1 & Vol. 2) by Lalit Sharma
- Applied Mathematics for Class 12 by R.S. Aggarwal.

Which Mathematics is tougher, the pure one or the Applied one?

Both the mathematics subjects are tougher in their own way. The science stream students study pure mathematics, it is tough and beneficial for them, and the Commerce and Arts stream students generally now opt Applied mathematics subject because it is beneficial for their future career options also. So , both are tough in their own respect fields.

Updated On : March 3, 2022

The Central Board of Secondary Education had developed a new elective course for the class 12 Commerce stream i.e. Applied Maths. Algebra is considered one of the main topics of applied maths in class 12.

In the CBSE Class 12 Board Exam, Algebra covers 10 marks out of 80 marks. This post takes you through detailed information about CBSE Class 12 Applied Maths Algebra.

As per the **CBSE Class 12 Applied Maths Syllabus** the main topics that you will be studying in Algebra are:

**Matrices:**In matrices, you will study the types of matrices, zero and identity matrices, transpose of a matrix, symmetric and skew-symmetric matrices, operation on matrices, simple properties of addition, multiplication, and scalar multiplication, the concept of elementary row and column operations, and etc.**Determinants:**In determinants, you will be studying the determinant of a square matrix (3x3 matrices), properties of determinants, minors, cofactors, and application of determinants in finding the area of a triangle, Adjoint and inverse of a square matrix, consistency, inconsistency, and the number of solutions of the system of linear equation by examples, and etc.- Cramer’s rule and its application.
- Simple applications of matrices and determinants including Leontief input-output model for two variables.

Read About **CBSE Class 12 Applied Maths Probability**

- You will get the best and easy understandable notes of Applied maths Algebra from the link provided in this article.
- The notes will include important CBSE Class 12 Algebra Questions.
- You will be getting the notes in both English as well as the Hindi Language. It is beneficial for you to study and understand the concept easily.
- The algebra topic holds a weightage of 13 marks in applied maths of class 12.
- The notes provided on this page have been made by experts and highly experienced teachers. The notes are made in simple language.
- You can download the CBSE class 12 Applied maths Algebra notes PDF by just clicking on the link provided on this page.

Read About **CBSE Class 12 Applied Maths Basic Financial with Mathematics**

You will be studying various topics in the Applied maths Algebra section that are Matrices, Determinants, Cramer’s rule and its application, and Simple applications of matrices and determinants including Leontief input-output model for two variables.

Knowing the syllabus will help you know important Applied Maths Algebra CBSE class 12 topics and focus more on those topics to score good marks in the exam. The table below shows the CBSE class 12 Applied Maths Algebra syllabus 2021:

Topics |
Explanation of Topics |

Matrices |
Concept of matrices, Notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication, and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (restricted to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). |

Determinants |
Concept of Determinant, Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors, and applications of determinants in finding the area of a triangle Adjoint and inverse of a square matrix Consistency, inconsistency, and number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using an inverse of a matrix |

Cramer’s rule and its Application |
Concept of Cramer’s rule and its Application, Derivation of application. |

Simple applications of matrices and determinants including Leontiff input-output model for two variables |
Concept of Simple applications of matrices and determinants including Leontiff input-output model for two variables. |

**Read about: ****CBSE Class 12 Linear programming**

To help you better understand the type of questions asked from the algebra topic, we have provided few sample questions here.

**Question 1: **Under what conditions on the real numbers a, b, c, d, e, f do the simultaneous equations ax + by = e and cx + dy = f have (a) a unique solution, (b) no solution, (c) infinitely many solutions in x and y. Select values of a, b, c, d, e, f for each of these cases, and sketch on separate axes the lines ax+by = e and cx+dy = f.

**Question 2:** For what values of a do the simultaneous equations x + 2y + a2z = 0, x + ay + z = 0, x + ay + a2z = 0 have a solution other than x = y = z = 0. For each such a find the general solution of the above equations.

**Question 3: **Do 2 × 2 matrices exist satisfying the following properties? Either find such matrices or show that no such exist.

- (i) A such that A5 = I and Ai 6= I for 1 ≤ i ≤ 4
- (ii) A such that An 6= I for all positive integers n
- (iii) A and B such that AB 6= BA
- (iv) A and B such that AB is invertible and BA is singular (i.e. not invertible)
- (v) A such that A5 = I and A11 = 0

**Question 4: ** (a) Find the remainder when n2 + 4 is divided by 7 for 0 ≤ n < 7. Deduce that n2 + 4 is not divisible by 7, for every positive integer n. [Hint: write n = 7k + r where 0 ≤ r < 7.] (b) Now k is an integer such that n3 + k is not divisible by 4 for all integers n. What are the possible values of k?

Read About **CBSE Class 12 Applied Maths Inferential Statistics**

Frequently Asked Questions

What is the weightage of Algebra section in Applied maths subject of class 12?

The Algebra section holds a weightage of 13 marks in Applied Maths subject of class 12.

What are the topics which will be taught in Applied Maths Algebra section class 12?

The topics which will be taught in Applied maths Algebra section class 12 are: -

- Matrices
- Determinants
- Cramer’s Rule and its Application
- Simple Applications of Matrices and Determinants including Leontiff input-output model for two variables.

What are the best reference books for the CBSE class 12 Applied Maths Subject?

The best reference books are: -

- Applied Mathematics for Class 12 (set of 2 Volume) by R.D. Sharma.
- Elements of Mathematics for Class XII (Vol - I & Vol –II) by M.L. Bhargava, Janardan Dinodia.
- A textbook of Applied Mathematics for Class 12 (Vol. 1 & Vol. 2) by Lalit Sharma
- Applied Mathematics for Class 12 by R.S. Aggarwal.

Which Mathematics is tougher, the pure one or the Applied one?

Both the mathematics subjects are tougher in their own way. The science stream students study pure mathematics, it is tough and beneficial for them, and the Commerce and Arts stream students generally now opt Applied mathematics subject because it is beneficial for their future career options also. So , both are tough in their own respect fields.