@RobertIsrael provided the correct answer. And there is no unique solution to the problem as stated. Will need to reformulate more carefully based on the use case: Suppose I'm in retail and I sell a number of SKUs that are oftentimes sold together. Each x is the cost of an individual SKU, but is unknown because of said bundling. The costs are a function of what's in A (which has M buyers of N SKUs), and b is the total dollars for each of my buyers. I want to find the average cost for each SKU.

For more context...Suppose I'm in retail and I sell a number of SKUs that are oftentimes sold together. Each x is the cost of an individual SKU, but is unknown because of said bundling. The costs are a function of what's in A (which has M buyers of N SKUs), and b is the total dollars for each of my buyers. I want to find the average cost for each SKU.

Thanks @RobertIsrael. I do want \begin{equation} |||Ax||_1 - ||b||_1|_1 \end{equation}. (the other would be l1 regression). The solution you proposed gives x as a scalar, correct? x is a vector, though. Rusty in my linear algebra, been quite a few years. Much appreciate the help