Linear Algebra Assignment Help




homework assignment help is most useful online portal for students providing all type of Online Linear algebra assignment help Services.Linear algebra is a branch of mathematics that studies vectors. Working according to certain rules, it mainly uses families of vectors called vector spaces or linear spaces, along with functions that input one vector and output another. Such functions that are well-behaved are called linear maps (or linear transformations or linear operators) and can always be represented by matrices. Linear algebra is central to modern mathematics and its applications. An elementary application of linear algebra is to find the solution of a system of linear equations in several unknowns. More advanced applications are ubiquitous in areas as diverse as abstract algebra and functional analysis. Linear algebra has a concrete representation in analytic geometry and is generalized in operator theory and in module theory. It has extensive applications in engineering, physics, natural sciences and the social sciences. Nonlinear mathematical models can often be approximated by linear ones.

Linear Algebra:

Linear Algebra usually consists of the linear set of equations as well as their transformations on it . It includes various topics such as matrices , vectors , determinants etc. Matrices and determinants are two very important topics of the linear algebra.

Linear Equations includes the topics mentioned as under :

  • Linear Equations

  • Matrices

  • Determinants

  • Complex numbers

  • Second degree equations

  • Eigen values / Eigen vectors

  • Vectors and its related operations

Linear Algebra : Description of Areas

Various Areas of algebra can be described as :

Linear Equations : It is an equation of first degree for example ,  2x + 5 = 9 . We have to solve it and find the value of unknown variable in it .

Matrices : They are usually expressed as an array of numbers . For example                       

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Determinants : It is a term which is calculated for each and every possible matrix . It defines the nature of the matrix.

Complex numbers : They are used to represent complex variables onto the space For eg : 2 + 3i where 2 is the real part and 3i is the complex part.

Second degree equations : They are often called as the quadratic equations. various methods are used to solve them like factoring , by making the square , the quadratic formula etc are present in linear algebra.

Eigen values : These are the scalars which are associated with the linear set of equations also known as the characteristic values and used with respect to matrices .

Vectors and its related operations : Vectors are the entities having both magnitude as well as direction. Different operations can be applied on it l;ike addition , subtraction , multiplication etc.

Applications of Linear Algebra

Linear algebra has a major number of applications . It is one of the very essential branch of mathematics . Some of its applications are :

  • Constructing curves

  • Least square approximation

  • Traffic flow

  • Electrical circuits

  • Determinants

  • Graph theory

  • Cryptography

Introduction to linear algebra made easy:

Linear algebra is a division of math concerned with learns of vectors, with families of vectors recognized vector spaces and by purpose to input one vector also output another, according to definite rules. These functions are identified linear chart and are frequently signify by matrices. Linear algebra is essential to made easy for modern math and its applications.

Linear Algebra:

An elementary function of linear algebra is to the resolution of systems of linear equations in some indefinite. More difficult applications are everywhere, in areas as different as abstract algebra and efficient analysis. Linear algebra has an existing representation in systematic geometry and made easy for common in operator theory. It has wide applications in the usual math. Nonlinear arithmetical form can frequently be approximated through linear ones.

Example for Algebra made Easy:

Example 1:

Find the x and y value intercept for the equation given 6y - 8 = 10x + 16 calculate made easy linear algebra

Solution:

 the given equation in slope intercept form,      6y - 8 = 10x + 16

6y  = 10x + 16+8

  6y = 10x+24

Divide the value 2 on both sides of the above equation, we get

          3y = 5x +12

           y = (5)/(3) x + (12)/(3)

          y = (5)/(3) x + 4

To find y intercept value, we take x value as zero (x = 0),

           y = 0 + 4

           y =4

To find the x intercept value, we take y value as zero (y =0).

          0 = (5)/(3) x + 4

Subtract the value 1 on both sides of the equation, we get

     (5)/(3) x = -4

         x= (-4*3)/(5)

      x =  (-12)/(5)

         x =(-12)/(5)

       x = -2.4

the values are x =-2.4 and y = 4

Example 2:

Find the x and y value intercept for the equation given 4y + 8 = 12x +20 calculate made easy linear algebra.

Solution:

  the given equation in slope intercept form,

                   4y + 8 = 12x +20

Subtract the value 6 on both sides of the above equation, we get

   4y = 12x+20-8

             4y = 12x-12

Divide the value 4 on both sides of the above equation, we get

             y = 3x +3

To find y intercept value, we take x value as zero (x = 0),

             y = 0 + 3

             y =3

To find the x intercept value, we take y value as zero (y =0).

          y = 3x +3

     0 = 3x+3

Subtract the value 1 on both sides of the equation, we get

        3x = -3

       x = -1

     the values are x=-1 and y = 3

Linear algebra:

    Linear algebra is a branch of math deals with linear equations, solving system of equations. These functions are called linear maps or linear algebra transformations and its represented by matrices. The linear algebra is linear equations, matrixes, determination, vector, vector space etc.  Linear algebra has a concrete symbol in analytic geometry and be a general in operator theory. It has extensive applications in the natural and the social sciences.

Linear Algebra Example 1:

Solve for x: x - 6= 10

Solution:

x - 6 = 10

Add 6 to both side of the equation

x- 6 + 6= 10 + 6

x = 16

The answer x is 16

Linear Algebra Example 2:

Solve for y: y + 8 = 15

Solution:

y + 8 = 15

Subtract 8 from both sides of the equation

y + 8 – 8 = 15 – 8

y = 7

The answer y is 7.

Linear Algebra Example 3:

Solve for x: x – 1/2 = 5/2

Solution:

x – 1/2 = 5/2

Add 1/2 to both sides of the equation

x = 5/2 + 1/2

x = 6/2

x = 3

The answer x is 3

Linear algebra Example 4:

Solve for x: 5 x - 6 = 3 x – 10

Subtract 3x from both sides of the equation

5x – 3x – 6 = 3x – 3x – 10

2x – 6 = - 10

Add 6 to both sides of the equation

2x – 6 + 6 = - 10 + 6

2x = - 4

Divided by 2 both side of the equation

x = - 2

The answer x is – 2

Linear algebra Example 5:

Solve for x: 4 x - 6 = 12 x – 40

Solution:

4 x - 6 = 12 x – 40

Subtract 4x from both sides of the equation:

4x – 4x – 6 = 12x – 4x – 40

6 = 8x – 40

Add 40 to both sides of the equation

-6 + 40 = 8x – 40 + 40

36 = 8x

Divided by 8 both side of the equation

x = 4.5

The answer x is 4.5

Linear Algebra Example 6:

Solve for x: x - 8= 10

Solution:

x - 8 = 10

Add 6 to both side of the equation

x- 8 + 8= 10 + 8

x = 18

The answer x is 18

Linear Algebra Example 7:

Solve for x: x - 5= 10

Solution:

x - 5 = 10

Add 6 to both side of the equation

x- 5 + 5= 10 + 5

x = 15

The answer x is 15

Introduction to learn linear algebra sample:

Learn linear algebra sample involves the process of solving sample linear algebraic expressions for learning. Generally the main function of the linear algebra is to find the unknown variable values from the system of linear expressions. Linear algebra maintains relation with the families of vectors called vector spaces. Linear algebra test preparation has the basic representation in analytical geometry and it is generalized in operator theory. The following are the sample problems in linear algebra to learn.

Linear Algebra Sample Problems to Learn:

Example 1:

Simplify the sample linear algebraic equation.

 -3(x - 2) - 4x - 1 = 2(x + 5) - x

Solution:

Given
-3(x - 2) - 4x - 1 = 2(x + 5) - x

Multiply factors
-3x + 6 - 4x - 1 = 2x + 10 - x

Grouping the above terms
-7x + 5 = x + 10

Subtract 5 to both sides
-7x + 5 - 5 = x + 10 -5

Grouping the above terms
-7x = x + 5

Subtract x to both sides
-7x - x = x + 5 -x

Grouping the above terms
-8x = 5

Multiply both sides by -1/8
          x = - 5/8

Conclusion:
          x = - 5/8 is the solution to the given equation

Example 2:

Simplify the sample linear algebraic equation.

              -5(x + 2) = x + 9

Solution:

Given
-5(x + 2) = x + 9

Multiply factors in left term
-5x - 10 = x + 9

Add 10 on both sides
-5x - 10 + 10 = x + 9 + 10

Grouping the above terms
-5x = x + 19

Subtract x on both sides
-5x - x = x + 19 -x

Grouping the above terms
-6x = 19

Multiply -1/6 on both sides


          x = -19/6

Conclusion:
            x = -19/6 is the solution to the given equation

Linear Algebra Practice Problems to Learn:

1) Simplify the sample linear algebraic equation.

-3(x - 2) - 2x - 3 = 2(x + 1) - 4x

Answer: x = 1/3 is the solution.

2) Simplify the sample linear algebraic equation.

            -2(x + 3) = x + 6

Answer:  x = -4 is the solution.



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