NCERT Solutions for Class 12 Maths Chapter 4 Determinants

Determinants have a number of applications in algebra. The concept of determinants is very useful for solving a set of linear equations. With determinants it becomes easier to understand the change in area, volume, and the change in variables in terms of integrals. Determinants are used for calculating the values of square matrices.

You can expect sums for solving linear equations from the topic of Determinants. There are various proofs that can be derived using the theory of determinants, so you can expect several ‘prove that’ sums from this topic in your exams. Also, for certain sums, you may have to find the values of some unknown variables using determinants and their resultant values.

Yes, you can download the NCERT Solutions for Class 12 Maths Chapter 4 for free from Vedantu. The NCERT Solutions for this chapter are provided in a PDF file on Vedantu. You can refer to these solutions online or download them and practice offline. All you need for downloading the NCERT Solutions of Class 12 Maths Chapter 4, Determinants, is an internet connection and a digital screen. Also, you can print a hardcopy of these NCERT Solutions for your convenience.

NCERT Solutions for Class 12 Maths Chapter 4 covers an important topic called Determinants. It is an easy chapter but it is quite lengthy and has a few problems to solve. It also has exercises for students to solve. The first exercise has eight questions, the second consists of 16 problems, with a few sub-questions. The third and the fourth exercise consist of five problems each. The fifth one is a bit longer and consists of 18 questions. The sixth exercise consists of 14 questions and the final miscellaneous exercise has 19 questions to solve.

NCERT Class 12 Maths is the prescribed textbook for the Maths syllabus. It is the first book one must cover before jumping into any other reference books. It strictly follows the syllabus of NCERT, and questions will be set based on this in the examination. Vedantu’s NCERT Class 12 Maths Solutions is also based on this book and has solutions for all the problems. Whenever there is any doubt, one can easily refer to these solutions so that no time is wasted searching for the answers.

Determinant is an important topic, from the examination point of view and education point of view. This topic is pretty easy and is a very useful one. Students will learn how to use determinants to check the system of linear equations and their consistency. Using determinants, one can express a linear equation and can solve it using the opposite of a coefficient matrix. Students will also learn the method of calculating the area of a triangle using determinants.

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NCERT Class 12 Maths is one of the most important subjects for a Class 12 student. It builds on some of the most critical concepts for the future of Mathematics and Physics. These topics are essential from the competitive exam point of view as well. There are a total of 13 chapters that are a part of the syllabus for Class 12. Students can use Vedantu’s Class 12 Solutions for Maths to avoid confusion or waste time while studying when stuck at any problem.

Please remember the following key rules for determinants in Class 12 Maths:-

• Determinants can only be calculated for square matrices, where the number of rows equals the number of columns. 

• Determinants help determine if a system of equations has one unique solution. 

• Swapping two rows (or columns) changes the sign of the determinant. 

• If any two rows or columns are identical, the determinant becomes zero. 

• Multiplying all elements in a row (or column) by a constant multiplies the determinant by that same constant.

• Scalar or First-Order Determinants: These are single-element matrices or determinants with only one row and one column.

• Minor or Second-Order Determinants: These are determinants obtained by removing either a row or a column from a square matrix.

• Cofactor or Third-Order Determinants: These are determinants obtained by multiplying each element of a row or a column by its cofactor and summing up the products.

The symbol used for determinants is denoted by

• Vertical Lines: This is shown as two vertical lines on either side of the matrix. For example, if you have a matrix A, the determinant would be written as |A|.

• Det(A): This is a shorthand way of writing "determinant of A".

The determinant is a scalar, which is a single number like 5 or -2. It has a magnitude (how big it is) but no direction. Determinants perfectly fit this definition. They are single numbers calculated from a square matrix, representing a specific property of that matrix.

The number of exercises on determinants class 12 solutions can vary depending on the edition and publisher. These solutions are typically not available in a strictly digital format that allows for easy counting. However, based on what students typically encounter, class 12 determinants NCERT Solutions for determinants likely cover a range of problems to help you practice and understand the concept thoroughly.

There are two main approaches to solving determinant problems, depending on the size of the matrix:

For 2x2 Matrices: Use a simple formula that multiplies opposite corners together and subtracts the product of the other two elements.

For 3x3 Matrices: This method involves more steps. Here's a simplified breakdown:

• Expand by a Chosen Row or Column: Pick a row or column in the matrix.

• Calculate Minor: For each element in that row/column, calculate a minor which is the determinant of a smaller matrix you get by excluding that element's row and column.

• Multiply by Cofactor: Multiply each minor by its corresponding cofactor, which is either 1 or -1 based on its position (a pattern you'll learn in NCERT solutions).

• Sum the Products: Add up all the products from step c to get the final determinant.

Use of Determinants class 12 solutions have several applications in algebra. They are very useful for solving a set of linear equations, making it easier to understand the change in area, volume, and variables in terms of integrals. Determinants are also used to calculate the values of square matrices.

This chapter will likely include problems that require you to use determinants to solve a given set of linear equations. From the standpoint of the exam, proofs that can be obtained from the theory of determinants and "prove that" sums are also significant. In some issues, you should use determinants and their resulting values to find the values of unknown variables.