Consider a system of linear equations of the form \mathbf{A}\mathbf{x}=\mathbf{b}, \mathbf{

sacateundisco8i3

sacateundisco8i3

Answered question

2022-02-24

Consider a system of linear equations of the form
Ax=b,ARL×K,xRL,bRK
with L variables x1,x2,,xLR and KL equations.
We are interested in finding a solution for a single variable x_l. Is there an explicit condition for existence of a unique solution for this variable?
Example: if x1+2x2+3x3=3 and 2x2+3x3=2, then there exist a unique solution x1=1 for the variable x1, and we cannot find unique solutions for the other variables.

Answer & Explanation

Ollie Castillo

Ollie Castillo

Beginner2022-02-25Added 5 answers

Yes, assuming that there is at least one solution, the condition is that the null-space of A has zero projection on the lth

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