Answer:
Because [tex]x = y[/tex], then the solution is unique.
Step-by-step explanation:
Given
[tex]Ax = b[/tex]
[tex]Ax=0[/tex]
See comment for complete question
Let there be two solutions x and y.
Such that:
[tex]Ax = b[/tex] and [tex]Ay = b[/tex]
Since:
[tex]Ax = Ay = b[/tex]
Then:
[tex]Ax - Ay = b - b[/tex]
[tex]Ax - Ay = 0[/tex]
This implies that:
[tex]Ax - Ay = A(x-y) = 0[/tex]
The only trivial solution is:
[tex]Ax - Ay = A(x-y) = 0[/tex]
Such that:
[tex]x -y = 0[/tex]
Then
[tex]x = y[/tex]
Because [tex]x = y[/tex], then the solution is unique.
