Translation of the Ax=0 solution set yields the Ax-b solution set since Ax-b is consistent. The Ax = b solution set is therefore a single vector if and only if the Ax = 0 solution set is a single vector, which occurs if and only if Ax 0 has only the trivial solution.
Finding the solution to an equation is like finding the solution to a puzzle. A mathematical equation proves the equality of two algebraic expressions. Determine the values of the variables that make the equation a true statement in order to solve an equation. An equation's solution is any value that causes the equation to be true.
given
Let's suppose that there is a solution to the equation ax = b.
Now, we want to demonstrate that the trivial solution exists for the equation ax = b when ax = 0.
Ax = 0 is homogeneous.
In the event that this equation was true for b, we define
To be a set of vectors with the form ax = b
w = m + gh
The subscript "h"
A solution to ax = 0 is gh.
Ax=b is in the form of w= m+gh based on the information we know had.
with
m = ax=solution b's
Soulution of gh = ax=0
Only a simple solution, ax = 0, exists.
gh = 0
where gh = 0
The relationship between ax=b and w=m
Ax = b thus has no alternative solutions.
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