What is the Matrix ?

What is the Matrix? 
In the end what you are first and formostly experiencing & battling with is your own belief system. Separating mind from matter, 'the world around you', and the physical was part of the creation of the illusion which would become the prison.

Therefore what the Matrix really boils down to is a belief that there's a Matrix/prison outside you, separate from you, toward which you are powerless.
At 2:48 Morpheus clearly says "It is a prison for your mind".
And in the beginning (@1:16) Morpheus gives it away when he asks Neo if he believes in fate, or thus not being in control of his own destiny.

The matrix is your belief there is a matrix outside of you which is in control of you. 

A thought process which keeps you focused on something outside of you and keeps you fighting 'it' or attaching to 'it', not seeing your own thought process/belief itself.

People locked up in physical prisons just make you believe the prison is 'out there', just like addicts,  due to which you will never figure out that your own mind is being used by you to imprison you ...that you are a slave of yourself. That the warden of your prison is you yourself.

Nobody will fight u harder than yourself for freeing yourself.
That's now the best place to hide the prison, from ourselves, i.e., in your own mind, and make ourselves the very warden of our own prison.
No other prison could in the end be able to sustainably keep everyone locked up.

In the absence of true purpose we need plans

The real work is to let go and just flow with the river. When we do this true purpose unfolds. Planning and strategizing is fighting the flow. The piece of art will make itself better than we ever could. it will come from within. Planning is mechanical. The flow is love. Just be in love with it. Be nature's instrument. let it show you what it wants to be. The great writer Edwardo Galeano, when writing his greatest works said...the story picked him to tell it to the world. Michelangelo would free the image from the stone. it was already in the stone. the true artist just masters a language with which s/he can help us see/hear/feel the muses. we need to live life like an artist. the true artist creates by letting go. strange things happen, even logistically when we stop resisting.

Choice vs Free Will

Purpose (what people refer to mostly as destiny) is from within, something we choose and have chosen to come here and fulfill (even before we came), not something that befalls us against our will. The essential Q is what is (really) free will? No one will stop you from 'choosing' any path (for instance one different to your true purpose). But technically speaking that is not free will. So choice is not yet free will. I can choose something but it is not yet free will. The core is if it comes from within or without (meaning the prompt). we can be manipulated into choosing something or a path. The 'idea' of true purpose would be connected to real free will meaning unconditioned. Coming truly from within and thus from ourselves and not from without/others. Only a real individual can exersize free will (technically speaking). The word destiny is a tricky one here for it is linked to predestination and fate and can be construed as something happening beyond ones choice. true purpose is quite the opposite.