Let y1(t) = t^2 and y2(t) = t|t| (a) Show that y1 and y2 are linearly dependent on the interval 0<=t<=1. (b) Show that y1 and y2 are linearly independent on the interval -1<=t<=1. (c) Show that the Wronskian W[y1,y2] is identically zero. My attempt: (a) So I know that if the Wronskian is zero, then y1 and y2 are linearly dependent. So i worked out the wronskian and i got w[y1,y2](t) = t^3 - t^2|t| I'm not sure how to show that it is linearly dependent on the interval. should i substitute in the intervals 0 and 1 and find that they are equal to zero? what about everything inbetween 0 and 1? (b) So for linearly independence, wronskian doesn't equal zero, again i have the same question of whether i substitute in the interval, and what do i do with the numbers inbetween, i am unsure how to prove this. (c) i have no idea what identically zero means, can someone explain this?