I was wondering how can I test these hypothesis simultaneously:

Ho: x1<>0 ; x2=0 ; x3=0

Ha: x1=0 ; x2<>0 ; x3<>0

I do not want to do sequential tests, like test for x1 first, then x2, and so on.

I know I can use the General Linear Hypothesis to test things like:

Ho: x1=0, x2=0, x3=0

Ha: x1<>0, x2<>0, x3<>0

But in my case, I have a mix of = and <>.

Any help will be appreciated. Thanks!