Hi,

I'm currently trying to understand the general solution to a system of linear equations in vector form. Let's say that when the system is in row reduced matrix form, there is a column will all zeros. According to the image that I took from a textbook, a zero column would suggest the existence of a free variable:

Based on this, can someone please let me know what the general solution in vector form look like? I thought it would be this:

However I'm skeptical since I thought that x_{3}would be represented somewhere in here, like how x_{5}was (in other words, I thought that all the free variables were present in the general solution in vector form so I'm confused where x_{3}is given that x_{3}is a free variable).

Please let me know!!!

- otownsend