If you have a system fo linear equations, the solution is where the equations intersect Using ro

Jamelia Daniels

Jamelia Daniels

Answered question

2022-02-17

If you have a system fo linear equations, the solution is where the equations intersect
Using row reduction you get a system of linear equations which still satisfies the intersection
Why are free variables used?
The values in which the free variable can be are limited in a range as for if the solution is a line and not a plane
So what is the point in writing the solutions as a set of vector additions using free variables?
If z in this case is a free variable, writing the solution in a vector equation
Where , denotes a new row
Solving for the pivot variables x and y and writing into decomposed vector form
[x,y] = [4,0] - [0,3] + z[1,2]
Z is said to be any real number zeR But looking at the graph, when z = 4, y=11/8 is not on the line of intersection So why do they say that z is a free variable when it isnt?

Answer & Explanation

Derrick Woods

Derrick Woods

Beginner2022-02-18Added 6 answers

The idea of free variables is that every free variable can have any value whatsoever, so they are really FREE. Once the values of the free variables have been chosen, there is no more freedom at all. The values of the remaining variables are completely determined by those of the free variables. So the free variables are totally free and the non-free variables are totally imprisoned.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?