Question

Suppose has a solution. Explain why the solution is unique precisely when has only the trivial solution. Choose the correct answer.

Answer 1

Answer:

Because $x = y$, then the solution is unique.

Step-by-step explanation:

Given

$Ax = b$

$Ax=0$

See comment for complete question

Let there be two solutions x and y.

Such that:

$Ax = b$ and $Ay = b$

Since:

$Ax = Ay = b$

Then:

$Ax - Ay = b - b$

$Ax - Ay = 0$

This implies that:

$Ax - Ay = A(x-y) = 0$

The only trivial solution is:

$Ax - Ay = A(x-y) = 0$

Such that:

$x -y = 0$

Then

$x = y$

Because $x = y$, then the solution is unique.