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# Maths Matrices and Determinants Chapter - Maths JEE Main

Last updated date: 04th Aug 2024
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## Concepts of Maths Matrices and Determinants for JEE Main Maths

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 Chapters 2024

### Important Topics of Matrices and Determinants Chapter

• Matrices

• Square Matrix

• Matrix Operations

• Matrix Multiplication

• Elementary Operation of Matrix

• Properties of Determinant

• Determinant of a 3 x 3 Matrix

## Matrices and Determinants Important Concepts for JEE Main

### 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.

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

### JEE Main Matrices and Determinants Solved Example:

1. If A=$\begin{bmatrix} 2 & 5 & -1 \\ 4 & 1 & 3 \\ \end{bmatrix}$ and B =$\begin{bmatrix} 3 & 2 & 4 \\ -1 & 5 & 2 \\ \end{bmatrix}$,

then A + B  = $\begin{bmatrix} 2 & 5 & -1 \\ -1 & 5 & 2 \\ \end{bmatrix}$ +$\begin{bmatrix} 3 & 2 & 4 \\ -1 & 5 & 2 \\ \end{bmatrix}$

=$\begin{bmatrix} 2+3 & 5+2 & -1+4 \\ 4-1 & 1+5 & 3+2 \\ \end{bmatrix}$

=$\begin{bmatrix} 5 & 7 & 3 \\ 3 & 6 & 5 \\ \end{bmatrix}$

2. If A = $\begin{bmatrix} 1 & 3 & -2 \\ 4 & 7 & 5 \\ \end{bmatrix}$

and B =$\begin{bmatrix} -2 & 1 & -1 \\ 3 & 5 & 2 \\ \end{bmatrix}$

then A-B = A+(-B) =$\begin{bmatrix} 1 & 3 & -2 \\ 4 & 7 & 5 \\ \end{bmatrix}$ + $\begin{bmatrix} 2 & -1 & 1 \\ -3 & -5 & -2 \\ \end{bmatrix}$

= $\begin{bmatrix} 1+2 & 3-1 & -2+1 \\ 4-3 & 7-5 & 5-2 \\ \end{bmatrix}$

= $\begin{bmatrix} 3 & 2 & -1 \\ 1 & 2 & 3 \\ \end{bmatrix}$

3. If A=$\begin{bmatrix} 1 & 1 \\ 0 & 2 \\ 1 & 1 \\ \end{bmatrix}$ and B  = $\begin{bmatrix} 1 & 2 \\ 2 & 2 \\ \end{bmatrix}$,

Then

AB = $\begin{bmatrix} 1 & 1 \\ 0 & 2 \\ 1 & 1 \\ \end{bmatrix}$ $\begin{bmatrix} 1 & 2 \\ 2 & 2 \\ \end{bmatrix}$

=$\begin{bmatrix} 1\times 1+1\times 2 & 1\times 2+1\times 2 \\ 0\times 1+2\times 2 & 0\times 2+2\times 2 \\ 1\times 1+1\times 2 & 1\times 2+1\times 2 \\ \end{bmatrix}$ $\begin{bmatrix} 3 & 4 \\ 4 & 4 \\ 3 & 4 \\ \end{bmatrix}$

4. Find the determinant of matrix A, if A=$\begin{bmatrix} 2 & 5 \\ 1 & 3 \\ \end{bmatrix}$

Solution: |A|= $\begin{bmatrix} 2 & 5 \\ 1 & 3 \\ \end{bmatrix}$

(2 x 3) - (5 x 1) = 6 - 5 = 1

5. Solve for det(A) which is $\begin{vmatrix}5 &2 &1 \\-2 &-1 &1 \\-4 &4 &3 \end{vmatrix}$

For solving det(A), row 1 shall be expanded

That being said, the expanded version of this determinant is given below

5$\begin{vmatrix}-1 &1 \\ 4 & 3 \end{vmatrix}$   -2$\begin{vmatrix}-2 &1 \\ -4 & 3 \end{vmatrix}$ + 1$\begin{vmatrix}-2 &-1 \\ -4 & 4 \end{vmatrix}$

This step involves solving for the 2x2 determinant matrices

5 { (-1 x 3) - (4 x 1)}  - 2 { ( -2 x 3 ) - ( 1 x -4)}  + 3 {(-2 x 4) - ( -1 x -4)}

5 ( -3 - 4) - 2 (-6 + 4) + 3( -6 -4)

5(-7) -2(-2) +3(-10)

= -35 + 4 -30 = -61

## JEE Main Maths - Matrices and Determinants Study Materials

Here, you'll find a comprehensive collection of study resources for Matrices and Determinants designed to help you excel in your JEE Main preparation. These materials cover various topics, providing you with a range of valuable content to support your studies. Simply click on the links below to access the study materials of Matrices and Determinants and enhance your preparation for this challenging exam.

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

## JEE Main Maths Study and Practice Materials

Explore an array of resources in the JEE Main Maths Study and Practice Materials section. Our practice materials offer a wide variety of questions, comprehensive solutions, and a realistic test experience to elevate your preparation for the JEE Main exam. These tools are indispensable for self-assessment, boosting confidence, and refining problem-solving abilities, guaranteeing your readiness for the test. Explore the links below to enrich your Maths preparation.

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## 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.

## FAQs on Maths Matrices and Determinants Chapter - Maths JEE Main

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. How can I effectively prepare for the Maths JEE Main Matrices and Determinants chapter?

Focus on understanding basic concepts, practice solving problems regularly, and consider utilising online platforms like Vedantu for personalised guidance and doubt resolution.

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.

4. What are the key topics covered in the Maths JEE Main Matrices and Determinants chapter?

The chapter includes essential topics like matrix operations, determinants, properties of matrices, and their applications in solving linear equations and transformations.

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