Question 4
A) Let there be a non-homogenous set of linear equations in 4 variables such that the vectors, $u_1=(1,-2,4,3), u_2=(-3,1,2,1), u_3=(2,-3,3,-2), u_4=(1,3,-10,-4)$ are it's solutions. Find the general solution of this system.
A lot of us weren't sure how to answer this question, or even exactly what they were asking for. Here's a general outline of what I did, but I'm pretty sure it's mostly wrong.
The given implies that there is a matrix $A_{m\times4}$ and some vector $b\in\mathbb{F}^m$ such that $Au_i=b$ for each $u_i$.
I then checked that the given vectors where L.I. and then wrote a general solution as being any linear combination of the given vectors. I already know that's wrong because the zero vector isn't a solution.
So is anything I wrote correct, and what is the correct answer?