Positive Linear Relationship with example

Introduction:

         Positive linear relationship is the part comes under linear algebra. The relationship explains the basic relations between the variables in the algebraic expression. A fundamental function of linear algebra is to determine the solution of systems of linear equations with some unknowns by the basis of known variables.

        Linear relationship has a demonstration in analytical geometry and is generalized in operational theory. Linear relationship positively associates with the families of vectors called vector spaces or linear spaces, and with functions contains one input vector and output vector, according to certain rules.

Example Problems for Positive Linear Relationships:

Ex:1 Reduce the linear relationship in the equation.
     -3(-z - 6) = 3z - 23
Sol: Given
-3(-z - 6) = 3z - 23
Multiply the factors in left term
3z + 18 = 3z - 23
Subtract 18 on both sides
3z + 18 - 18 = 3z - 23 - 18
Grouping the above terms
3z = 3z - 41
Subtract 3x on both sides
3z – 3z = 3z - 41 -3z
By solving the above term

0z = -41

There is no real value for z, so the above equation has no solutions.