If is a linear transformation such that
Let me explain my thinking first:
so a(1+2x)+b(3+5x) = -2 - 3x
I solved and got that a = 1 ; b = -1
I then did:
1(2-3x) + -1(2-3x) = 0.
The homework system I'm using only allowed me one try on the problem, and so I want to make sure that I did it correctly, however, my gut tells me 0 is not the right answer. Is my instinct right or am I doubting myself?
Any help would be greatly appreciated, I only have one attempt and I'd like to get it right!