JEE Important Chapter - Matrices and Determinants
What are Matrices and Determinants?
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
JEE Main Maths Chapter-wise Solutions | |||
1 | 9 | ||
2 | 10 | ||
3 | Matrices and Determinants | 11 | |
4 | 12 | ||
5 | 13 | ||
6 | 14 | ||
7 | 15 | ||
8 | 16 | ||
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
Important Concepts of Matrices and Determinants
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.
$A= \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix}$
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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.
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.
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FAQs on JEE Important Chapter - Matrices and Determinants
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.
