Linear Algebra Unique Solutions

Posted on February 27, 2012. Filed under: Uncategorized | Tags: , , |

Previously we have discussed about how to find the area of a hexagon and In today’s session we are going to discuss about Unique solution Linear Algebra, It is studied in context of solving the equations of Linear Algebra. To find the solution of a pair of equations, draw it on the graph and if they meet at only one point then such solution of equation is called the unique solution of the linear equation.

Linear Equation is the equation in which we have equations in two variables. To solve these equations we have various methods.

First method to solve the equation of Linear Algebra is the method of substitution.

Unique solution Linear Algebra is the set of two linear equations which have only one common point . These two equations intersect at only point when we draw such lines on the graph.

Let us assume any system of linear equations say

ax + by + c = 0 and dx + ey + g = 0

This set of equations from will have a unique solution if the two lines which are represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at only one point. Through this we directly come to the conclusion that these set of lines are not parallel.

Also if they are not a pair of parallel lines, the two lines should have different slopes.
We also conclude from this:
ax + by + c = 0 and dx + ey + g = 0 will not represent two parallel lines if their slopes are different.

I.e. when the ratio of coefficient of x and y are not equal. It implies:

(a / d ) <> (b / e)

In the next session we will discuss about Finding Solution of Simultaneous Equations by Graphing and You can visit our website for getting information about math helper online and cbse in nic.

 

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