Mathematics, has one interesting, important and easy topic named Matrices? Each year you do get two to three questions in all the important exams across the globe, if your concepts are clear, it will be of great help in other important topics like integrals and calculus and concepts like axis transformation. The part of the syllabus in class 12th appears as a totally new subject which makes it a little challenging for some of the students in the initial stages. When you keep solving more problems from this chapter and get familiar with the ideas and concepts, you realize how easy it is to solve almost all the questions from this chapter.
LEARN THE CHAPTER AND SOLVE QUESTIONS OF MATRICES
Determinants and Matrices discover a varied range of applications in actual life problems, as in the software of adobe photoshop it is used to render images using the linear transformation process. Matrices are used for computer programming to encrypt the messages, for storing data in the folders, executing queries and resolving the problems of Algorithms, etc. Robotics also uses calculation-based matrices to program the movement of a robot.
The techniques and concepts of Matrices are valuable when we start doing algebra, it is vital to carefully cover everything in the chapter. Though, there are several sub-topics you must certainly not omit while studying the chapter. The critical ones are mentioned here for your reference:
- Operation of matrices
- Kinds of matrix
- Skew-symmetric and symmetric matrix, Transpose
- Skew-Hermitian and Hermitian matrix, Conjugate
- Matrix Determinants
- Cofactor and Minor of component of determinant/matrix
- Inverse and Adjoint
- Use of Elementary row operations to find the inverse of the matrix
- Cramer’s rule and linear equations system
- Homogeneous systems of linear equations
Matrix method and Gaussian Elimination Method also called Row reduction are two important methods to Solve linear equations.
Finding solutions to the arrangement of equations using the matrix method is as follows:
- The variables in all equations should be appropriately written.
- The constants and coefficients of the variables should be written on the sides respectively.
To solve a system of linear equations by the technique of discovering the inverse
- Matrix A: variables representation
- Matrix B: constants representation
Matrix multiplication can help in solving an arrangement of equations
Now let’s look at how to use the Gaussian Elimination method to find the solution.
- We write the augmented matrix for linear equations.
- Use the elementary approach so that all elements under the chief diagonal are zero. When we obtain a zero diagonally, a row operation should be performed to obtain a nonzero element.
- We find the solution using back substitution.
Tips:
- This chapter is not only about numerical or inverse of matrix, the concepts of the theory must be also clear to you.
- It is vital to understand the determinants and their properties.
- Before you are going for your exam, be very clear in your mind about the style of expanding the Determinants.
The generalization of Matrices can be done in various ways. Algebra makes use of matrices by entering in general fields and rings, whereas in linear algebra the arrangement of properties of matrices is in the linear map concept. Matrices have the possibility of considering infinite rows and columns. The extension of tensors is another one, that is often seen as higher-dimensional arrangements of numbers, as conflicting to vectors, which can be realized as arrangements of numbers. In some cases of firm requirements matrices have a tendency to form groups that are called matrix groups. Likewise, matrices that form rings under desired conditions are called matrix rings. Some matrices also form fields which are called matrix fields.
Like other chapters of mathematics, this chapter also requires a lot of practice, and the best data available online is from Cuemath, you are sure to clear all your doubts and score well if you go through their explanations and the tips and suggestions provided here.
