This course teaches matrix algebra from beginner level to pro-level. Here we have tried to design this course in such a way that a proper understanding can be developed in students who learn it. The unique feature of this course is that it can make you curious to learn more and enable to use your knowledge for academic purposes as well as for understanding day to day problem where matrix algebra can be used to find solutions.
Matrix algebra is actually a different language which runs parallelly with other mathematical methods. The same mathematical problem you solve using different mathematical formulae becomes altogether a very simple and attractive when solved using rules of matrix algebra. We have also used Excel and R-software to solve problems. The aim was to update students with the current developments taking place in this field.
Why do we study matrix and what is the meaning of matrix?
How mathematical operations are done using matrix algebra.
With very colorful boxes without leaving a single step, each concept of matrix algebra has been illustrated.
Answers to students questions are also given within a 4-days time.
If you want to become an instructor, you can join us.
Use of EXCEL and R Software is also taught in this course for matrix algebra.
What is the target audience?
From 10th standard onwards, every student can enroll for the course.
Teachers who teach it to various class can also enroll.
The course duration depends on the time devoted and learning speed of the student.
For adding two or more matrices, we simply add the corresponding elements of both the matrices. That is, we take the first element, a11, of matrix A and add it to the first element, b11, of matrix B. This is called element-wise addition or 'vector recycling'.
The first step in matrix multiplication is to take the first row of the first matrix A (pre-multiplication matrix) and multiply each element of that row one by one by the corresponding elements of the first columns in matrix B.
Calculating Covariance and Properties of Covariance
Calculating Matrix' mean, variance and standard deviation.
To calculate the mean of a matrix having mxn dimension, calculate the mean of each column because each column is a different variable; then, use these means to find out variances and S.Ds of each variable or column respectively.
For a 2x2 matrix, we do not first construct the matrix of minor and then change the sign to make the cofactor matrix, which is later transposed to make an adjoint matrix. Here, the same operations are implemented easily and the adjoint of a 2x2 matrix is found directly making the following adjustments:
Cofactor matrix and Adjugate/Adjoint of a 3×3 matrix
Cofactor matrix and Adjugate/Adjoint of a 3x3 matrix
Finding the cofactor and adjugate or adjoint of a 3x3 matrix involves many steps and is a bit lengthy. We use a procedure known as Laplace or cofactor expansion.
Practically speaking, (1) we find out 3x3= 9 determinants from a 3x3 matrix and arrange them into a rectangular box. After this, (2) we put a positive or negative sign in front of each element of that rectangular box, according to rules given below, to make it a cofactor matrix.
If row + column = an even number, then use a (+) sign in front of the number.
If row + column = an odd number, then use a (-) sign in front of the number.
(3) When the cofactor matrix is calculated, we transpose it to make adjugate or adjoint matrix.
Elements of an inverse matrix are just the quotients obtained solving the fraction having an element of the adjugate/adjoint matrix as a numerator and the determinant of the matrix in the denominator. Since it is a 2 x 2 matrix having 4 elements, then we have to divide each of these 4 elements in the numerator one by one having the determinant of the matrix in the denominator.
There are three steps involved in calculating the inverse of a 3x3 matrix as we did in the case of computing the inverse of a 2x2 matrix, but, here, the procedure is not very straight forward as we experienced in a 2x2 matrix and is a bit lengthy in terms of execution of each step.
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