if equations 2x-y+z=0 ,x-2y+z=0 and tx-y+2z=0 have non trivial solutions and f(x)be continuous functions such that f(5+x)+f(x)=2 then integrate f(x) dx (limit 0 to -2t)
Here are some hints to get you started.
First find the determinant of this matrix and set it equal to zero and solve for
For the 2nd part use the linearlity of the integral to break it up into two parts
Then make a u-substitution.
Good luck and post your workings if you get stuck.