Electronis Discussion
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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?

  1. Both I and II are true
  2. Both I and III are true
  3. Both II and IV are true
  4. Both III and IV are true
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