In the middle of the 19th Century, Arthur Cayley (1821-1895), an English mathematician created a new discipline of mathematics, called matrices. He used matrices to represent simultaneous system of equations. As of now, theory of matrices has come to stay as an important area of mathematics. The matrices are used in game theory, allocation of expenses, budgeting for by-products etc. Economists use them in social accounting, input-output tables and in the study of inter-industry economics. Matrices are extensively used in solving the simultaneous system of equations. Linear programming has its base in matrix algebra. Matrices have found applications not only in mathematics, but in other subjects like Physics, Chemistry, Engineering, Linear Programming etc.

In this lesson we will discuss different types of matrices and algebraic operations on matrices in details

OBJECTIVES

**After seeing this video you will be able to:**

- define a matrix, order of a matrix and cite examples thereof;
- define and cite examples of various types of matrices-square, rectangular, unit, zero,l diagonal, row, column matrix;
- state the conditions for equality of two matrices;
- define transpose of a matrix;
- define symmetric and skew symmetric matrices and cite examples;
- find the sum and the difference of two matrices of the same order;
- multiply a matrix by a scalar;
- state the condition for multiplication of two matrices; and
- multiply two matrices whenever possible.
- use elementary transformationsl
- find inverse using elementary trnsformations

EXPECTED BACKGROUND KNOWLEDGE

- Knowledge of number system
- Solution of system of linear equationsl

MATRICES AND THEIR REPRESENTATIONS

Suppose we wish to express that Anil has 6 pencils. We may express it as [6] or (6) with the understanding that the number inside [ ] denotes the number of pencils that Anil has. Next suppose that we want to express that Anil has 2 books and 5 pencils. We may express it as [2 5] with the understanding that the first entry inside [ ] denotes the number of books; while the second entry, the number of pencils, possessed by Anil.

OBJECTIVES

**After seeing this video you will be able to:**

- define a minor and a cofactor of an element of a matrix;

- find minor and cofactor of an element of a matrix;
- find the adjoint of a matrix;
- define and identify singular and non-singular matrices;
- find the inverse of a matrix, if it exists;
- represent system of linear equations in the matrix form AX = B; and
- solve a system of linear equations by matrix method.

EXPECTED BACKGROUND KNOWLEDGE

- Concept of a determinant.
- Determinant of a matrix.
- Matrix with its determinant of value 0.
- Transpose of a matrix
- Minors and Cofactors of an element of a matrix.

DETERMINANT OF A SQUARE MATRIX

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