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# JEE Important Chapter - Matrices and Determinants

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## What are Matrices and Determinants?

Last updated date: 18th Sep 2023
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Matrix and Determinant is one of the most intriguing, simple, and significant subjects in mathematics. Every year, at least 1 - 3 problems from this chapter will appear in JEE Main and other entrance examinations. This chapter is completely new from the student's perspective, as it will be covered in 12th grade.

Determinants and matrices are used to solve linear equations by applying Cramer's rule to a collection of non-homogeneous linear equations. Only square matrices are used to calculate determinants. When a matrix's determinant is zero, it's known as a singular determinant, and when it's one, it's known as unimodular. The determinant of the matrix must be nonsingular (i.e., its value must be non-zero) for the system of equations to have a unique solution. Let us look at the definitions of determinants and matrices, as well as the various types of matrices and their properties, using examples.

## JEE Main Maths Chapter-wise Solutions 2023-24

### Important Topics of Matrices and Determinants

• Matrices

• Matrix Addition

• Square Matrix

• Matrix Operations

• Matrix Multiplication

• Elementary Operation of Matrix

• Properties of Determinant

• Determinant of a 3 x 3 Matrix

## Definition of Matrix

Matrices are a type of ordered rectangular array of numbers used to represent linear equations. There are rows and columns in a matrix. On matrices, we can execute mathematical operations such as addition, subtraction, and multiplication. The number of rows and columns in a matrix represents the order of the matrix. Let there are m rows and n columns in a matrix, then its order will be m x n.

$A= \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix}$

Answer: 0

### Conclusion

In this article, we have elaborated on concepts and solutions to questions on the topic Determinants and Matrices. We have also learn how to find determinant of a matrix (determinant of a matrix formula) and properties of matrices and determinants. Everything you're looking for is available in a single location. Students can carefully read through the concepts, definitions and questions in the PDFs, which are also free to download and understand the concepts used to solve these questions. This will be extremely beneficial to the students in their exams.

## Study Materials for Matrices and Determinants:

These study materials will aid you in comprehending Matrices and Determinants, ensuring a solid foundation for further mathematical pursuits.

 Matrices and Determinants Related Study Materials Matrices and Determinants JEE Main Notes Matrices and Determinants JEE Main Important Questions Matrices and Determinants JEE Main Practice Paper

## Important Links for JEE Main and Advanced 2023-24

Access a curated collection of study materials and tips to excel in JEE Main and Advanced 2023-24, helping you prepare effectively for these prestigious engineering entrance exams.

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## JEE Main Important Dates

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JEE Main 2023 January and April Session exam dates and revised schedule have been announced by the NTA. JEE Main 2023 January and April Session will now be conducted on 24-Jan-2023 to 31-Jan-2023 and 6-Apr-2023 to 12-Apr-2023, and the exam registration closes on 12-Jan-2023 and Apr-2023. You can check the complete schedule on our site. Furthermore, you can check JEE Main 2023 dates for application, admit card, exam, answer key, result, counselling, etc along with other relevant information.
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## JEE Main Information

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JEE Main 2023 Study Materials: Strengthen your fundamentals with exhaustive JEE Main Study Materials. It covers the entire JEE Main syllabus, DPP, PYP with ample objective and subjective solved problems. Free download of JEE Main study material for Physics, Chemistry and Maths are available on our website so that students can gear up their preparation for JEE Main exam 2023 with Vedantu right on time.
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## JEE Main 2023 Book Solutions and PDF Download

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## JEE Main 2023 Cut-Off

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## JEE Main 2023 Results

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## FAQs on JEE Important Chapter - Matrices and Determinants

FAQ

1. What is the order of matrices and determinants?

A matrix has an order of m x n because it has m rows and n columns, whereas a determinant has an order of n x n because it has n rows and n columns( it should have an equal number of rows and columns).

2. Who is the father of matrices?

Arthur Cayley, known as the "Father of Matrices," was a brilliant mathematician. On August 16, 1821, he was born. In 1858, Arthur Cayley presented the conceptual explanation of the matrix in his Memoir on the Theory of Matrices. As a result, matrices became one of the most important branches of mathematics in the research. He primarily worked on Algebra and was instrumental in the establishment of the modern British pure mathematics school.

3. What are the unique uses of matrices and determinants?

The matrix has numerous applications in data science and artificial intelligence. The matrix inversion method can be used to solve a large number of algebraic equations. A matrix's transpose, adjoint, and inverse can also be found.