Introduction to linear Algebra:
The bunch of mathematics that handles with the theory of systems of number systems , matrices, vector spaces, determinants, and linear equations.
A mathematical package and vector space with scalars from a related field, the multiplication of which is of the method (aA) (bB) = (ab) (AB), here scalars are a and b and vectors are A and B.
Description about linear algebra with application:
In linear algebra the following types are used, they are
Matrices and Systems of Equations
Determinants
Vector Spaces
Linear transformations
Orthogonally
Eigenvalues
Numerical linear algebra
Iterative methods
Descriptions:
Matrices and systems equations:
Its Rectangular array of real numbers
It contains m rows by n columns
It should be Named using capital letters
The First subscript is row, second subscript is column
Determinants
The determinant is defined as a special method related with any square matrix. The basic geometric, the determinant is defined as scale factor for calculating if the matrix is consider as a linear transformation.
Vector Spaces
It’s a mathematical calculated shaped by a group of vector: objects will be connected together and multiplied ("scaled") by figures, called scalars.
Orthogonality
It’s a relation of opposition between the things at right angles and it’s a quality of lying or intersecting at right angles
Numerical linear algebra
By using this technique we can easily perform the linear algebra calculations. Here we used some algorithms to find out the matrix operations. It is also used to perform the fundamental engineering concepts and some science related problems.
Application of linear algebra with solutions
The following applications are used in the linear algebra , they are
Application 1 - Its used to find the Least Square approximation
Application 2 -We can use the linear algebra in Traffic Flow, Electrical Circuits and Determinant
Application 3 -We can build the curves and surfaces which is passing the given the particular points.
Application 4 -In inheritance, its widely used to discover the solution,
Application 5 -We can use the technique in cryptography and graph theory.
Solve the solution for following linear equation.
1) 7x-6 = 3x-8
Step1: here subtract 3x from both the sides, we get
Solution:
7x-3x-6 = 3x-3x-8
4x-6 = -8
4x = -8+6
4x = -2
x= -1/2
x =-1/2
The bunch of mathematics that handles with the theory of systems of number systems , matrices, vector spaces, determinants, and linear equations.
A mathematical package and vector space with scalars from a related field, the multiplication of which is of the method (aA) (bB) = (ab) (AB), here scalars are a and b and vectors are A and B.
Description about linear algebra with application:
In linear algebra the following types are used, they are
Matrices and Systems of Equations
Determinants
Vector Spaces
Linear transformations
Orthogonally
Eigenvalues
Numerical linear algebra
Iterative methods
Descriptions:
Matrices and systems equations:
Its Rectangular array of real numbers
It contains m rows by n columns
It should be Named using capital letters
The First subscript is row, second subscript is column
Determinants
The determinant is defined as a special method related with any square matrix. The basic geometric, the determinant is defined as scale factor for calculating if the matrix is consider as a linear transformation.
Vector Spaces
It’s a mathematical calculated shaped by a group of vector: objects will be connected together and multiplied ("scaled") by figures, called scalars.
Orthogonality
It’s a relation of opposition between the things at right angles and it’s a quality of lying or intersecting at right angles
Numerical linear algebra
By using this technique we can easily perform the linear algebra calculations. Here we used some algorithms to find out the matrix operations. It is also used to perform the fundamental engineering concepts and some science related problems.
Application of linear algebra with solutions
The following applications are used in the linear algebra , they are
Application 1 - Its used to find the Least Square approximation
Application 2 -We can use the linear algebra in Traffic Flow, Electrical Circuits and Determinant
Application 3 -We can build the curves and surfaces which is passing the given the particular points.
Application 4 -In inheritance, its widely used to discover the solution,
Application 5 -We can use the technique in cryptography and graph theory.
Solve the solution for following linear equation.
1) 7x-6 = 3x-8
Step1: here subtract 3x from both the sides, we get
Solution:
7x-3x-6 = 3x-3x-8
4x-6 = -8
4x = -8+6
4x = -2
x= -1/2
x =-1/2
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