Linear algebra

Hello, I'm currently doing part b) and getting a little stuck.

My instinct says that I need to write 5 equations, such as x(1) = 2 + s + t and then use the 5 equations to find s, t and then x(1) to x(5)?

Well, the question explictly tells you to form 5 inequalties, so I'd say your instincts are wrong. (I also have no idea where 2 + s + t came from!).

Your first inequality should be: "Since $x_1 = 2 + s - t$, and $x_1 \geq 0, \, 2 + s - t \geq 0$".

For how to proceed after you have the 5 inequalities, you just have to look for ways to find conditions on s and t that eventually allow you to find them.

Ahh I don't know what I'm doing... I've followed your example and completed the other 4 inequalities, but I don't really know what you mean by finding conditions for s and t other than that they are both greater than or equal to 0 and I don't know what using that fact does for me.

Unfortunately your hint of x(2) + x(3) >= 0 hasn't helped me much... x(2) + x(3) = -10t... so -10t >= 0.

If -10t >=0, what can we say about t? And what else do we know about t? So...

If -10t>= 0 then t has to be negative to be greater than 0, but we also know t is greater than 0, so we have a contradiction?

Having s also = 0 give me the correct answer, but I don't know how to prove s = 0 from the other side, just that I know s>=0