Mathematics is a subject that is considered very tough and boring by a lot of students. The reason behind this is the lack of clarity on basic concepts of mathematical topics. Once you understand the concept, mathematics learning becomes easy as well as interesting. Mathematics tuition has become necessary for students to build a strong foundation in mathematical concepts that will prove to be highly beneficial in the long run. Students get proper guidance for learning and developing their abilities in logical thinking and applying the same for problem-solving on mathematical topics.
Invertible Matrix: A Matrix With The Same Number of Rows And Columns
A matrix is an arrangement of numbers or quantities in a definite number of rows and columns. The number of rows and columns of a matrix is called dimensions. A square matrix has the same number of rows and columns. A square matrix is called an invertible matrix if the product of this matrix and its inverse matrix becomes an identity matrix. The determinant of an invertible matrix is always a non-zero quantity. An invertible matrix is also known as a non-singular matrix. Invertible matrix has a useful application in the encryption of messages particularly when coding has become a significant aspect in recent years.
Invertible Matrix Example
Suppose, there is a matrix P of dimension m x m (m denotes the number of rows and columns). Then the invertible matrix of P will be another matrix Q of the same dimension m x m such that the determinant of Q is not equal to zero and the product of P and Q is an identity matrix.
It can be expressed as, PQ = QP =I, where I denote the identity matrix.
If there can be two invertible matrices B and C for any square matrix A, then we can say B = C.
Cuemath website gives a very comprehensive idea about invertible matrices and their properties.
The Mathematics Tuition Methodologies
The mathematics tuitions supplement the classroom sessions by providing individualized attention to students and help in clarification of doubts. The expert mentors focus on improving the areas where the students lack knowledge and clarity on concepts. The methods applied in mathematics tuition must be simple yet effective in making students interested and engaged in learning. The tutors should focus on practice-oriented learning because mathematics deals with problem-solving and handling assignments. The method of tuition must align with the learning abilities of students and aim at creating a learning environment of fun and enjoyment so that children can never feel burdened. The use of real-life examples, models, quizzes, and puzzles is the best way to make students learn the basic concepts from an early age. For the students of higher grades, the use of worksheets and assignments helps to develop their problem-solving skills and confidence to handle any type of problem.
Online Mathematics Tuition
Online education in recent years has come up as an effective alternative to traditional education through classroom sessions. Students were apprehensive that online tuition might be not as useful as conventional mode but various learning management institutions have designed online tuition classes that have proven to be quite beneficial for students. The online learning apps offer both the students and teachers easy access to the online mathematics tuition using simple digital tools and techniques. The audio, video, and conference facilities help students to interact and share feedback just like live classroom sessions.
Invertible Matrix: Important Points
- The determinant of an invertible matrix can never be zero.
- The product of a given matrix and its invertible matrix gives the value 1.
- The invertible matrix of a square matrix is always unique.
- The invertible matrix is a given matrix of the same dimension.
Cuemath is one of the leading online platforms providing opportunities to students to avail of mathematics tuition as per their requirements.