Hey guys new here to the forum, I am just learning about linear algebra in college and can do the basics. My only problem is when we apply this knowledge to more abstract ideas, for example these two questions on chemistry and road maps.

I think I am on the right track with the first one, but I am completely stumped by the second, I have no idea how to attempt it.

For the first one (I must note I am no chemistry expert so forgive me if I'm completely wrong) but is it basically asking you to find a value for a,b,c,d and e such that:

aNaHC(O3)+b(H3)(C6)(H5)(O7)=c(Na3)(C6)(H5)(O7)+d(H 2)O+eC(O2)

???

from there i equated the amount of Na, H, C and O on each side such that:

Na: a=3c

H:a+8b=5c+2d

C:a+6b=6c+e

O:3a+7b=7c+d+2e

Then I moved everything onto one side of the 4 equations to we have:

(1)...a-3c=0

(2)...a+8b-5c-2d=0

(3)...a+6b-6c-e=0

(4)...3a+7v-7c-d-2e=0

With these 4 simultaneous equations, I constructed a matrix which I then solved in mathematica. It gave me b,c,d and e in terms of a. I assume this is because we have 4 equations but need 5 because we have 5 variables. so I guess the solution isn't unique and maybe I've answered my own question by myself?

Anyway I have no idea with the second. Thanks for your time everyone