Matrices And Determinants
Matrices and determinants were discovered and developed in the 18th and 19th centuries. Initially, their development dealt with the transformation of geometric objects and the solution of systems of linear equations. Historically, the early emphasis was on the determinant, not the matrix. In the modern treatment of Linear Algebra, matrices are considered first.
Matrices provide a theoretically and practically useful way of approaching many types of problems including; Solutions of system of linear equations, Equilibrium of rigid bodies, Graph theory, Theory of games, Leontief economics model, Forest management, Computer graphics and Computed tomography, Genetics, Cryptography, Electrical networks, etc.
Matrices are a very important tool in expressing and discussing problems which arise from real-life issues. Matrices are applied in the study of electrical circuits, quantum mechanics and optics, in the calculation of battery power outputs and resistor conversion of electrical energy into another useful energy.
Matrices play a major role in the projection of three-dimensional images into a two-dimensional screen creating the realistic seeming motion. Matrices are used in calculating the gross domestic products in Economics which eventually helps in calculating the production of the goods efficiently.
Matrices are the base elements for robot movements. The movements of robots are programmed with the calculation of matrices row and columns. The inputs for controlling robots are given based on the calculations from matrices. Matrices are also used in many organizations by scientists for recording data of their experiment.
This course is useful for students from Plus one course (CBSE and all State Syllabus) onwards
- Lectures 13
- Quizzes 0
- Duration 15 hours
- Skill level All levels
- Language English
- Students 3
- Certificate Yes
- Assessments Yes
Definition and formation of matrices
This session gives the definition of a matrix and explains how to form Matrices of different orders
Different types of Matrices and Equality of matrices
This session explains different types of matrices with examples and equality matrices
Operations on Matrices - Addition, Subtraction and Scalar Multiplication
How to add and subtract matrices and explains scalar multiplication
Multiplication of Matrices
Condition for multiplication of two matrices and explains how to multiply two matrices
Properties of Multiplication
Describes the associative and distributive law of matrices
Transpose of a Matrix
Explains Transpose and properties of Transpose of a matrix
Determinant of a Matrix
Explains Determinant and how to compute the determinant of a square matrix of different orders
Minors and Cofactors
Explains Minors and Cofactors with examples
Application of Determinants
Application of determinants - Area of a triangle and solution of two variable and three variable equations using determinants(Cramers rule)
Adjoint of a matrix
Inverse or Reciprocal of a Matrix
This session gives the definition of inverse of a matrix and explains how to find the inverse of a Matrix
Solution of equations using Matrices
Solution of two variable and three variable equations using Matrices
Evaluation of Results using Properties of determinants and mathematical Induction
This section explains how to prove results using Properties of determinants and Mathematical Induction