Solving a system of linear equations using back substitution

[Jen2114]

Hello,
its been a while since I have taken linear algebra and I am having trouble understanding what a target vector is. I need to solve a system of linear equations in matrix form using back substitution and with different target vectors. I don't have a problem with back substitution, but I don't recall exactly what a target vector is and how I would use it with back substitution to solve the system. Could someone help me clarify this concept? Thanks!

 

[FactChecker]

The only use of the term "target vector" that I have seen is where there is no feasible solution of the linear equations and a least squared error solution is desired.

But I imagine that there is no reason not to use that term also when there is an exact solution with no errors. In that case, a single solution with a single "target" vector would be the back-substitution process that you are familiar with.

Another possibility is that you are being asked to find a single vector of inputs that gives the best least-squared-error solution to multiple target vectors at the same time.

PS. The fact that I mention lease-squared-error is simply because that is the most common error minimization problem and a lot of effort has been exerted to find quadratic minimization algorithms to solve that problem. Other error metrics can also be used.