GATE ECE 2017 Set 1 | Question: 3

Question

Consider the following statements about the linear dependence of the real valued function $y_{1}=1,y_{2}=x$ and $y_{3}=x^{2}$ over the field of real numbers.

1. $y_{1},y_{2}$ and $y_{3} $ are linearly independent on $-1\leq x\leq 0$
2. $y_{1},y_{2}$ and $y_{3} $ are linearly dependent on $0\leq x\leq 1$  
3. $y_{1},y_{2}$ and $y_{3} $ are linearly independent on $0\leq x\leq 1$ 
4. $y_{1},y_{2}$ and $y_{3} $ are linearly dependent on $-1\leq x\leq 0$

Which one among the following is correct?

• A. Both I and II are true
• B. Both I and III are true
• C. Both II and IV are true
• D. Both III and IV are true