Parametrize the solution set of this one-equation system.

[Antonius]

The question: Parametrize the solution set of this one-equation system. x_1 + x_2 + ... + x_n = 0

My question (please look at the photo): I understood why we have the first row, but what's the point of the other rows?

 

[andrewkirk]

The answer is given as a subset of $\mathbb{R}^n$, with the representative element given as a vector that is expressed as a sum of n-1 vectors that span the (n-1) dimensional solution space.

Re-write that sum as a single vector, by adding component-wise, and you'll see how the rows work together to solve the problem.