I control the camera in my program by changing the transformation matrix (which alters the other underlying matrices). Not this is all in 2D.

The transformation matrix is pretty standard. It is a 4x4 matrix with the diagonal acting as the scale factor (x, y, z) and the right side acting as the offset coordinates (this is ignoring shear and rotation which aren't that important to me though I would like the method to still work with rotation).

So essentially I am currently zooming by altering the x and y scale in the transformation matrix. This seems to act from the top left corner (which is the origin in my coordinate space). I would like the zoom to act towards the mouse. So knowing the x and y position of the mouse when I apply my transformation (every frame)  how should I alter the zoom so that it zooms towards whatever the mouse position was?

I can share code if you would like but I am writing this in Rust. Also let me know if you need more information I am happy to provide I just didn't want to over share.

I can't change the origin it is too central to everything else in the engine. I generally want it to zoom to the mouse position. Which I can get each frame or during each "apply"

I'm not sure how you could use the translation part to simulate zooming?

Oh Okay I see what you mean. That actually won't work in my case. While the transformation matrix works like a general 3D one editing the z translation won't actually change anything about the view. 

The basic idea is to translate so the zoom center is at the origin, then scale, and then translate back.

But that should be equivalent to scaling and then translating by zoomCenter*scale-zoomCenter, or something like that.