How to calculate s1 and s2 for vector additions

Question

I have attached the question i need help with. I have solved from part a to part c, but dont really understand how to workout part d and part e, can someone please explain what those equations mean and how to go about solving them.

Answer 1

For (e) you have to solve:

$s_1(1,-2,1)+s_2(3,1,-2)=(5,1,-2)$.

We get the system

$s_1+3s_2=5$

$-2s_1+s_2=1$

$s_1-2s_2=-2.$

Can you proceed ?