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GATE EC 2017 Set 1 — Question 3

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MCQ+1 / -0.33EasyLinear IndependenceLinear AlgebraEngineering Mathematics

Engineering Mathematics → Linear Algebra → Linear Independence

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Question

Consider the following statements about the linear dependence of the real valued functions y1=1y_1 = 1, y2=xy_2 = x and y3=x2y_3 = x^2, over the field of real numbers.
I. y1,y2y_1, y_2 and y3y_3 are linearly independent on −1≤x≤0-1 \le x \le 0
II. y1,y2y_1, y_2 and y3y_3 are linearly dependent on 0≤x≤10 \le x \le 1
III. y1,y2y_1, y_2 and y3y_3 are linearly independent on 0≤x≤10 \le x \le 1
IV. y1,y2y_1, y_2 and y3y_3 are linearly dependent on −1≤x≤0-1 \le x \le 0Which one among the following is correct?
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