Matrices and Determinants have the distinction of being one of the easiest topics to score perfectly in JEE. Every year, students encounter at least 2-3 questions from this section. So what exactly are Matrices and Determinants? A Matrix is a rectangular array of numbers arranged in rows and columns. A Determinant of a Matrix is an unique number that can be determined for every square matrix. It is arrived at by adding and multiplying the numbers in the matrix. Matrices and Determinants are used to solve linear equations.They have wide applications in a variety of fields like electronics, economics, robotics, genetics, etc. When studying Matrices and Determinants, it is important for the student to know about all the different types of matrices and their properties. Some of the most commonly used types are Row Matrix, Column Matrix, Square Matrix, Diagonal Matrix, Vertical Matrix, Horizontal Matrix, Scalar Matrix, Singleton Matrix, etc. It is interesting to note that there is a possibility for a matrix to belong to more than one type. For example, a square matrix can also be a symmetric matrix or a diagonal matrix and vice versa. When the number of rows and columns in the matrix are exactly the same, the matrix can be called a square matrix. A transpose of a matrix is obtained by flipping the rows and columns of a given matrix. If the transpose of a matrix is the same as the original matrix, it is said to be a symmetric matrix. Since the elements in each position remain the same even when the rows and columns and rows are interchanged, the dimensions of the matrix remain the same. Hence, it is evident that a square matrix can also be classified as a symmetric matrix if it meets this special condition.
There are certain concepts and sub-topics in matrices that hold additional importance when it comes to solving questions that appear in engineering exams like JEE. For instance, It is necessary to know how to find the adjoint and inverse of a matrix in order to tackle some frequently repeated types of questions. As the name indicates, the inverse of a matrix can be understood as the reciprocal of that matrix. So when you multiply the original matrix and its inverse, you will end up with an identity matrix. The first step towards finding the adjoint of a matrix is to find the individual cofactors of all the elements in the matrix. The next step is to create the cofactor of the entire matrix using all the individual cofactors. The final step is obtaining the transpose of the cofactor matrix. If the matrix is denoted as A, then the adjoint of that matrix would be denoted as adj (A). A good understanding of basic linear algebra is also a prerequisite to comprehend and make quick progress in Matrices and Determinants.