linear independence 
Hey everyone, I'm having trouble with this problem. I set up two equations to be: $1+k = 0$ and $k + 2k+48$ and I got that k = -24 and or -1. But the answers don't work so my logic is clearly flawed. I think I'm going about this equation the wrong way. Any hints on how I should attack it? 

On way to do it is to observe that the vectors are linearly independent if $$\det\pmatrix{1 &k \\k & 2k+48}\neq 0$$ which gives you the equation $$2k+48-k^2\neq0 \iff -k^2+2k+48 \neq 0$$ or equivalently $$(k+6)(k-8)\neq0$$ which gives you that $a=-6, b=8$.
