Question

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disaproves the statement.

The inhomogeneous system of equations Ax=b, hwere b=/0, has either the trivial solution or an infinite number of the solutions.

Answer 1

We can say that is FALSE because the inhomogeneous sytem
`Ax =b` can present an unique solution
`x = A^(-1)b` if
`|A|\\eq 0`, so this is a good counter example on which we have a vctor that is not the trivial solution and we don't have an infinite number of solution.

Explanation:

For this case we can use the following definition:

Let
`A x = b` a linear system, this system is called homogeneous if
`b =0` and in other case is called inhomogeneous.

So then for the statement "The inhomogeneous system of equations Ax=b, where
`b\\eq0`, has either the trivial solution or an infinite number of the solutions."

We can say that is FALSE because the inhomogeneous sytem
`Ax =b` can present an unique solution
`x = A^(-1)b` if
`|A|\\eq 0`, so this is a good counter example on which we have a vctor that is not the trivial solution and we don't have an infinite number of solution.