Introduction
Matrices Role In Linear Algebra and play a dominant role in linear algebra. They may be used to efficiently represent systems of linear equations, and then they also represent linear functions or linear mappings. Before we talk over certain of these exciting topics, let us first describe what a matrix is and what kind of operations we can do with matrices.
History of the Matrix
The matrix has a lengthy history of application in explaining linear equations. They were identified as arrays while waiting for the1800‘s. The term matrix, named in Latin for womb, resultant from mater—mother was created by James Joseph Sylvester in 1850. He assumed a matrix as an object giving increase to a number of factors today known as minors, namely, determinants of minor matrices that are resulting from the unique one by eliminating columns and rows. The English mathematician, Cullis, used the modern bracket notation for matrices in 1913.He all at once confirmed the first important use of the notation A=ai,j to signify a matrix where ai,j states to the element found in the ith row and the jth column. Matrices may be used to efficiently write and work with many linear equations, mentioned to as a system of linear equations, at the same time. Matrices and matrix multiplication disclose their vital types when connected to linear transformations, also recognized as linear maps.
What is a Matrix?
A matrix in Mathematics is a rectangular array of numbers, symbols, and expressions that arranged in rows and columns. Matrices are usually written in box brackets. The horizontal and vertical lines of entries in a matrix are named rows and columns, correspondingly. The size of a matrix is well-defined by the number of rows and columns that it covers. A matrix with m rows and n columns is called an m × n matrix or m-by-n while m and n are called its dimensions.
Matrix Dimensions:
Every element of a matrix is frequently denoted by a variable with two subscripts. For example, a2, 1 a2, 1 signifies the element at the second row and first column of a matrix A. The single items in a matrix are called its elements or entries. Two matrices may be added or subtracted element by element if they have the same size
The rule for matrix multiplication, though, is that two matrices may be multiplied simply when the number of columns in the first equals the number of rows in the second. A number of matrixes may be multiplied element-wise by a scalar from its allied field.
Matrices which have an only one row are called row vectors. Those which have a single column are named column vectors. A matrix which has the identical number of rows and equal number of columns is known as a square matrix.
Types of operations
There are three types of operations that may be practical to modify matrices
Addition
Subtraction
Scaler multiplication
Adding and Subtracting Matrices
We practice matrices to list data or to signify systems. As the items are numbers, we may perform operations on matrices. We add or subtract matrices by adding or subtracting matching items.
Acceptable to do this, the entries must match up. So, addition and subtraction of matrices is only likely when the matrices have the same dimensions. Matrix addition is commutative and is also associative, consequently the below is correct:
A + B = B + A
A + B = B + A
(A+B)+C=A+ (B+C)
(A+B)+C=A+ (B+C)
Addition of matrices is very simple. Just add every element in the first matrix to the matching element in the second matrix. By way of we might estimate, subtracting works greatly the same way but that we subtract in its place of adding.
Scalar Multiplication
Scalar multiplication of a real Euclidean vector by a positive real number multiplies the level of the vector deprived of altering its direction in a natural geometrical context.
Linear equations
Matrices may be used to efficiently write and work with multiple linear equations. That is the systems of linear equations. As, if A is an m-by-n matrix, x calls a column vector that is, n×1-matrix of n variables x1, x2,…, xn, and b is an m×1-column vector, then the matrix equation.
