Until the 1800s, matrices were known as arrays. The term matrix came from the word womb (matter-mother) in the 1850s because he recognized matrix as an object which gave rise to determinants, also known as minors. Hence, we can say that determinants originally are derived from matrices, removing columns and rows from the source.
A matrix can be defined as a rectangular array of numbers. It is more like a “box” of numbers where you can track individual elements in the vertical direction(columns), as well as in the horizontal direction(rows). A matrix box contains a set of numbers or algebraic expressions. The concept of brackets in matrices was introduced by an English mathematician called Cullis in the year 1913. We can use matrices to work with a system of linear equations.
Since a matrix is an array of numbers, if the array consists of n rows and m columns, then it is called the n×m matrix. Here, the numbers n and m are dimensions of the given matrix. We usually denote matrices with capital letters, like X, Y, etc. However, in the case of a one-dimensional matrix, we sometimes use lower case letters.
We can perform addition, subtraction, multiplication, and even division (in some cases) on matrices. Although many calculators and computer programs can do matrix operations these days, learning how to do operations on Matrix is particularly important for the students.
Matrix is a remarkably interesting topic. You will be surprised to know that scientists and engineers represent equations as matrices so that they can have a systematic way of doing calculations. Computers have embedded matrix arithmetic in most of the graphics-processing algorithms for rendering reflection and refraction. These properties make matrices unique. Matrices are used in applied physics to study electrical circuits, optics, chemical engineering, aerospace engineering, and even quantum physics. All these fields need complex computations that can be obtained through matrix transformation. Not only these, but matrices are also used in hospitals, CAT scans, and MRIs to generate valid results.
Let us know now dive into the details and study various interactive ways through which we can understand matrices:
Learn the Addition and Subtraction of Matrices
Matrix addition is simple, and it is very similar to adding real numbers. The prerequisite required to perform the operations of addition or subtraction on matrices is that the given matrices have the same dimension or size. Having the same size or dimension means that they have the same number of rows and columns. If they don’t have the same size or dimension then the addition and subtraction of matrices cannot be performed.
Learn the Multiplication of Matrices
Matrix multiplication is not as simple as its addition and subtraction. You will need to understand all the conditions and follow the prescribed steps to get it right. Students find it difficult because it involves a lot of steps. But trust me, it is not tough at all. Once you understand the steps, it will be fairly easy for you to perform matrix multiplication and you might start enjoying it like a game.
You need to follow a stepwise approach to learn how to multiply matrices. If you are familiar with vector multiplication, matrix multiplication won’t be hard for you. Find out how to multiply matrices in this blog. This is a stepwise guide for the multiplication of matrices.
Understand Matrix Determinants
A matrix determinant is a special number that is used to find solutions to systems of linear equations and has applications in calculus as well. Matrix determinants play a key role in finding the inverse of matrices.
Here are some of the properties of the matrix determinant:
The determinant of Z or |Z| of a square matrix Z is a number encoding certain properties of the matrix Z. The symbol for the determinant of a matrix Z is |Z|. This symbol is also used for absolute value, although the two have nothing to do with each other. The determinants are named after the size of the matrices. For example, determinants of a 3 × 3 matrix are called third-order determinants.
Visualizing the Matrices
A matrix is just a big 2D array that holds information. It is more like animation software where you can animate not just the physical position of an object, but also animate its rotation about its axis. Also, a graph allows one to visualize a matrix and its inverse. With the help of a graph, we can visualize various properties of a matrix.
It is amazing how, with the help of technology, math can be taught in a fun and interactive way. You can create visual simulations with various tools that can help students see a real-time representation of matrices. Especially when it comes to complex concepts, like multiplication and division of matrices (in some cases). It also allows students to see the reasoning behind the concepts, which is quite motivating as learning concepts through a different perspective helps them gain new insights and understand the why behind what.
Games are the best way to understand complex concepts. Visualizing matrices can be tough, but playing games isn’t. If the students can learn matrices while engaging in games, then they can understand the concept better. There are a lot of games available online which can simulate a student’s mind. You can engage in fun games to understand matrices better.
Cuemath believes in crafting engaging experiences. They offer interactive math games that can make you understand the concept of matrices in a fun and engaging way. These games spark creativity and help you understand complex concepts with ease.
Activities and Tasks
The students can engage in tasks like researching some business or economics that can be represented as a simple matrix that can facilitate higher-level thinking. The research can include things like sharing data, GDP figures overtime, etc.
Group discussions can work great when it comes to understanding matrices. Students can create opportunities to work through problem sets in pairs or a group of three and four. This can help students to raise any queries that they might have. Collaboration helps a lot when students are learning matrices as this topic draws a lot of complementary threads. The students are likely to get immense benefit from brainstorming sessions with fellow students.
Students can also be encouraged to bring up any problem that they come across while exploring matrices and discuss them. This could give a hint to the lecturer or tutor regarding any common misunderstanding or areas of difficulty. The tutors can then plan their course of action to clarify the doubts.
Working in groups
By working in pairs or groups, you can create a PowerPoint presentation with your teammates summarising the key steps needed to solve matrices. This could also include working on the collected data and representing them in the form of matrices. You can also perform operations like addition, subtraction, multiplication of matrices on the collected data. This can help students clear their doubts and prepare them to take up more challenging problem statements.
Practice questions through worksheets
Once the students have mastered each of the steps (mentioned above), they will need to practice solving more problem statements to increase their confidence in the subject. Students should also be encouraged to develop their own questions and curate them in their personalized mini worksheets. Later, students can exchange their worksheets and solve the matrix problems curated by their peers. This is an excellent way to develop an understanding of the entire concept.
Understanding the Matrix Diagram
A matrix diagram is a new management planning tool that is generally used for analyzing and displaying the relationship between different data sets. The matrix diagram not only represents the relationship between the data sets but also provides relevant information about the relationship, for instance, the roles played by various individuals or measurements.
Solve sample problems Online
Solving sample matrix problems can help learn faster and more effectively. You can also find many sample matrix problems online that can help reinforce key concepts and help you test your knowledge. Solving sample problems can help you see more and reach further in your understanding of matrices. It can be challenging as well as motivating at the same time. Since it encourages you to be inquisitive and gain new insights rather than just solving what is served in the books, this is a recommended step.
I hope this blog was helpful and you enjoyed reading this. Would you like to add your tips and tricks to this list? Share your comments below!
by SaimKhan on 2021-01-21 01:30:42