  ## FUNDAMENTALS OF MATRIX AND DETERMINANT Trupti M. Gohil

### FUNDAMENTALS OF MATRIX AND DETERMINANT

Matrix calculus generalizes classical analytical notions such as derivatives and exponentials to higher dimensions. The graphics software uses the concept of a matrix to process linear transformations to render images.Matrices are used very often in 3D geometry (e.g. computer graphics) and are very powerful. A simple 4x4 matrix can represent a lot of transformations at once (translation, rotation, scaling, perspective/orthogonal projection). You can then multiply a 3D position vector (x, y, z, 1) by this matrix to obtain a new position with all the trasformations applied. Notice that this vector is also a 1x4 matrix (although the position is in 3D, the fourth component is added to make the multiplication possible and allow for the projection transformation, if you want to know more read about homogeneous coordinates). Similar ideas can be used in 2D or even in higher dimensions like 4D.

Benefits of Doing this course :

• Matrices are one of the most powerful tools in mathematics. The evolution of the concept of matrices is the result of an attempt to obtain compact and simple methods of solving the system of linear equations
• Most Scientific Fields have Applications of Matrices in some or the other form. Almost every branch of physics, including classical mechanics, optics, electromagnetism, quantum mechanics, and quantum electrodynamics, matrices are used to study physical phenomena, such as the motion of rigid bodies.
• In computer graphics, they are used to project a 3-dimensional image onto a 2-dimensional screen. In probability theory and statistics, stochastic matrices are used to describe sets of probabilities; for instance, they are used within the Page Rank algorithm that ranks the pages in a Google search.

• Maximum Duration to complete the Course: 1-Month
• Course Fees: Rs. 2500/- (Several Payment Options Available: Credit & Debit Cards, Cheque, Demand Draft, Cash, Wire Transfer – NEFT, PayTM)
• Online Evaluation Method: Based on “Multiple Choice Question (MCQs)” and an “Assignment Submission” of 500 words.
• The score of the online examination will be taken as final result and Grade will be assigned as per the following scheme: Grade A – 80-100, Grade B – 65-79, Grade C – 50-64, Reattempt – Below 50
• Next Batch: Each IALM course starts immediately after payment. Students can register online for the course any time. Upon payment of fees and registration, the present Course will start immediately.

Type Lesson Title Time
Introduction of determinant 6 Hrs
Examples of matrices 6 Hrs
Introduction of Matrices 6 Hrs
Example, operations and properties of matrices 6 Hrs
Example of matrix 6 Hrs
Various methods for finding inverse of matrix 6 Hrs
Assignment Questions 6 Hrs

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