Consider the following statements about the linear dependence of the real valued functions y 1 = 1, y 2 = x and y 3 = x 2 , over the field of real numbers. I. y 1 , y 2 and y 3 are linearly independent on – 1 ≤ x ≤ 0 II. y 1 , y 2 and y 3 are linearly dependent on 0 ≤ x ≤ 1 III. y 1 , y 2 and y 3 are linearly independent on 0 ≤ x ≤ 1 IV. y 1 , y 2 and y 3 are linearly dependent on – 1 ≤ x ≤ 0 Which one among the following is correct?

Correct Answer is : Both I and III are true

GATE Electronics and Communications (EC) 2017 Shift 1 Solved Paper

Question : 13 of 65

Marks: +1, -0

Consider the following statements about the linear dependence of the real valued functions y₁ = 1, y₂ = x and y₃ = x², over the field of real numbers.
I. y₁, y₂ and y₃ are linearly independent on – 1 ≤ x ≤ 0
II. y₁, y₂ and y₃ are linearly dependent on 0 ≤ x ≤ 1
III. y₁, y₂ and y₃ are linearly independent on 0 ≤ x ≤ 1
IV. y₁, y₂ and y₃ are linearly dependent on – 1 ≤ x ≤ 0
Which one among the following is correct?

Both I and II are true
Both I and III are true
Both II and IV are true
Both III and IV are true

Validate

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