A Comprehensive Guide to Solving Equations with Matrices

Jul 15, 2021

Many students find difficulties in math especially solving equations with matrices. Before going inside the topic, it is very important to know what a matrix is. A matrix is a rectangular arrangement of columns and numbers in a row. This rectangular arrangement of numbers is encircled by large brackets [ ] or small brackets ( ). In addition, matrices are generally with capital letters like A, B, C, D, etc., and its factors are with small elements a, b, c, d, etc.

For example: A= [1, 6, 8], B= (a, b, c)

These equations of matrices are easy for those who know the trick to solve. But most of the students face difficulties in solving the equations quickly. If you are one of them, then do not worry. You are in the right place to solve your issues with math. Here you can get a comprehensive guide to solving equations with matrices.

Go through Matrix Theorems:

If you feel difficulties in solving equations with a matrix, one reason can be a lack of basic knowledge of matrix theorems. The Matrix theorem guides you through matrix multiplications, matrix addition, transposition rules, inverse rules, and many others. You need to understand and remember the rules of matrix algebra, which can help you to solve the matrix.

Did you know? If you have an understanding of the basics of the matrix, you can solve any kind of matrix problem in a simple way. And, your basic knowledge will enhance your solving equations with the matrix.

Understand the types of matrices:

After understanding the basic rules of matrices, it is essential to understand the different forms of matrices. In the matrices chapter, you have to go through the types like Row matrix, square matrix, Column matrix, scalar matrix, unit matrix, Singleton matrix, Singular matrix, equal matrix, Triangular matrix, Null or zero matrices, and Diagonal matrix.

While solving the equations with matrices, you can find any types of questions related to these matrices’ types. So you need to differentiate these types while attempting the question. Even you need to understand some tricks to solve the matrix equations. Additionally, a simpler matrix equation can be solved easily by using scalar multiplication and matrix addition.

Understand the problem or question:

Many students don’t try to deeply understand the questions due to exam time limitations or some other reasons. This is the reason students fail to solve the matrix questions. There is a lack of understanding of the matrix question.

Therefore, when you are sitting to solve a math problem, don’t get scared by seeing the question itself. And, don’t get panicked
about the time limitation. You need to read the matrix question twice or thrice. Here, you need to give time and try to think in which way you can solve the questions. For sure, you will find the answer.

Do more practices:

You must have heard that practice makes a man perfect. Yes, more practice can make you perfect in solving matrix problems. Even you can feel confident while solving the problems related to the matrix. Sometimes students are unable to manage their time and don’t opt for the matrix questions at exams. But here, more practice will make you better at solving the matrix equations, and this will help you manage the time during the exam.

If you want to solve the matrix equation, you need to give more time to this chapter. And you have to increase the matrix equation practices.

Involve yourself in group studies:

Many people think that group studies are a waste of time. Many say students don’t read and practice in group studies. But it is not exactly true. There are many students who want to learn something new every day. They don’t want to waste their time. If you are one among them, then group studies are the best method to gain knowledge. And it improves the student’s critical thinking and problem-solving skills.

If you want to improve your solving matrix equation speed, you can ask your friends for group studies. Here you can involve some bright students and some average students and form a group to learn among each other. Also, you can learn some solving techniques from your friends.

Do Self-Practice or Individual practice:

Even if you do group practice for solving the equation with the matrix, you need to give separate practice time to it. Often, students forget the methods and tricks to solve the equations that they learned from their friends in group studies.
This problem will not occur if you write down the techniques and methods to solve questions as well as practice them at your home. Self-practice is an excellent method for improving your problem-solving skills.

Contact your faculties/ teachers:

Sometimes students get stuck in some of the matrix problems where they need the help of an expert. Well, all are not a genius in solving the equations of the matrix. At some point in time, you need the help of a teacher or faculty.
If you gave enough time to solve an equation but still do not find any outcomes, you must contact your faculty. They are experts in these chapters as they are teaching the same for a long time.

MOCK test:

MOCK test stands for Multiple Option Checking Test. This test is helpful for the students to practice many types of matrix questions. Even many experts say that nowadays, it is very important to appear in a MOCK test before appearing in the final exams. This MOCK test helps us to understand the exam pattern, different types of questions, and many other things.

If you want to improve your problem-solving skills in the matrix, then you must go for the MOCK test. It can help you to overcome mistakes and enhance your confidence to solve the equations of the matrix.


Through this post, you got a comprehensive guide to solving equations with matrices. After reading this post, you must have got an idea of how you can solve equations and the correct approach to studying. If you follow the same guide, you can be a professional one day in solving equations with matrices. So, keep practicing to be better.

Article Posted in: Information and Examples


Sid writes educational content periodically for Wizert and backs it up with extensive research and relevant examples. He's an avid reader and a tech enthusiast at the same time with a little bit of “Arsenal Football Club” thrown in as well. He's got more than 5 years of experience in technical content framing, digital marketing, SEO and graphic designing.

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