Respuesta :
Answer:
We can say that is FALSE because the inhomogeneous sytem [tex] Ax =b[/tex] can present an unique solution [tex] x = A^{-1}b[/tex] if [tex]|A|\neq 0[/tex], 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.
Step-by-step explanation:
For this case we can use the following definition:
Let [tex] A x = b [/tex] a linear system, this system is called homogeneous if [tex] b =0[/tex] and in other case is called inhomogeneous.
So then for the statement "The inhomogeneous system of equations Ax=b, where [tex] b\neq0[/tex], has either the trivial solution or an infinite number of the solutions."
We can say that is FALSE because the inhomogeneous sytem [tex] Ax =b[/tex] can present an unique solution [tex] x = A^{-1}b[/tex] if [tex]|A|\neq 0[/tex], 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.
