What is Matrices:-
Introduction
Certain branches of mathematics such as Linear Algebra and Group Theory use block of matrices while dealing with the problems of social sciences, physical science, biological science and engineering sciences. The ancient Chinese appreciated the advantages of array manipulation in dealing with systems of linear equations, which might have germinated a genuine theory of matrices. From the middle 1600s to the middle 1800s, while Europe was flowering in mathematical development, the study of array manipulation was exclusively along with the study of determinatnts. It was not untill the work of the British mathematician Arthur Cayley(1821-1895) that the matrix was singled out as a separate entity, distinct form the notation of a determinatnt. this laid the foundation for the modern theory of matrix analysis and linear algebra. today, matrix theory occupies a central position in pure as well as in applied mathematics.
In this blog, I shall be concerned matrices as a rectangular arrays of real or complex numbers(called scalars) and algebraic operations defined on them.
Matrix:-
A Matrix is a rectangular array of numbers arranged in formation of rows (horizontal lines) and columns (vertical lines) enclosed within the square brackets [ ] or parenthesis ( ).
A matrix is said to be real or complex according as its elements are real or complex.
for instances,
\[i). \left[\begin{array}{cc} 3 \end{array}\right] \\\] \[ii). \left[\begin{array}{cc} 3&4&5 \\ 1 & 2 &2 \end{array}\right]\] \[iii).\left[\begin{array}{cc} 3 & 4 & 5 \\ 1 & 2 & 2 \\ 2 & 3 & 4 \end{array}\right]\] \[iv).\left[\begin{array}{cc} a & b \\ p & q \\ r & s \end{array}\right]\]
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