The study of linear sets of equations and the transformations they undergo together is called Linear Algebra. While Learning Linear Algebra we come across many topics like, Systems of Equations, Matrices, Determinants, Euclidean n-space, Vector Spaces and Eigen Values & Eigen Vectors. These topics can be learnt with ease using many courses offered as online course Linear Algebra.
Math Linear Algebra
In this article we shall learn in brief about system of equations and matrices. The general linear equation is given by a1x1+ a2x2+ a3x3+…..+ anxn = b; here there are n unknowns and the known numbers are x1, x2, x3…xn . The solution set of which would be given by the set of numbers s1, s2, s3….., sn such that if we equate x1= s1, x2=s2, x3=s3….., xn=sn then the equation is satisfied.
This means that when the solution set values are substituted on the left hand side of the equation that would be equal to the value b on the right hand side. Solving system of equations involves different methods in which use of matrices is one of them. Some of the methods are used in solving the systems of linear equations are Gaussian Elimination and Gauss-Jordan Elimination. A series of steps in this method help in solving the given equations.
Let us now take a quick look at Matrices, a matrix is a rectangular array of numbers in the form of rows and columns and each of these elements is called an ‘entry’. The size of any given matrix is denoted with n rows and m columns using nxm. For instance, 3x4 shows it is a matrix consisting of 3 rows and 4 columns.
The matrix that has only one column is called a column matrix (vector) and the one which has only one row is called a row matrix. A matrix is denoted using an upper case letter and the entries using lower case letters. The entry in the ith row and jth column is denoted as ‘aij’ when the matrix considered is ‘A’. A square matrix is the one which has equal number of rows and columns and is denotes as nxn.
In a square matrix the entries a11, a22…ann which form the numbers in a diagonal is called the main diagonal of the matrix. This article gives a very brief outline of Matrices. To learn and understand the various topics under linear algebra with ease and to get Linear Algebra homework help there are many online courses that are offered to one and all.
Math Linear Algebra
In this article we shall learn in brief about system of equations and matrices. The general linear equation is given by a1x1+ a2x2+ a3x3+…..+ anxn = b; here there are n unknowns and the known numbers are x1, x2, x3…xn . The solution set of which would be given by the set of numbers s1, s2, s3….., sn such that if we equate x1= s1, x2=s2, x3=s3….., xn=sn then the equation is satisfied.
This means that when the solution set values are substituted on the left hand side of the equation that would be equal to the value b on the right hand side. Solving system of equations involves different methods in which use of matrices is one of them. Some of the methods are used in solving the systems of linear equations are Gaussian Elimination and Gauss-Jordan Elimination. A series of steps in this method help in solving the given equations.
Let us now take a quick look at Matrices, a matrix is a rectangular array of numbers in the form of rows and columns and each of these elements is called an ‘entry’. The size of any given matrix is denoted with n rows and m columns using nxm. For instance, 3x4 shows it is a matrix consisting of 3 rows and 4 columns.
The matrix that has only one column is called a column matrix (vector) and the one which has only one row is called a row matrix. A matrix is denoted using an upper case letter and the entries using lower case letters. The entry in the ith row and jth column is denoted as ‘aij’ when the matrix considered is ‘A’. A square matrix is the one which has equal number of rows and columns and is denotes as nxn.
In a square matrix the entries a11, a22…ann which form the numbers in a diagonal is called the main diagonal of the matrix. This article gives a very brief outline of Matrices. To learn and understand the various topics under linear algebra with ease and to get Linear Algebra homework help there are many online courses that are offered to one and all.
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