Question

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

Answer 1

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

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.