Question

Notify Me Bookmark

Determine whether the given set of functions is linearly independent on the interval (-inf, inf). f1(x) = x, f2(x) = x^2, f3(x) = 3x - 6x^2

Determine whether the given set of functions is linearly independent on the interval (-inf, inf). f1(x) = x, f2(x) = x^2, f3(x) = 3x - 6x^2

Image text
Determine whether the given set of functions is linearly independent on the interval (-inf, inf). f1(x) = x, f2(x) = x^2, f3(x) = 3x - 6x^2

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Answer
Doubtrix Logo

This Problem has been solved!

You'll get a detailed, step-by-step and expert verified solution.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Login Sign Up

Similar/Related Questions

Determine whether the given set of functions is linearly independent on the interval (-inf, inf). f1(x) = e^x, f2(x) = e^-x, f3(x) = sinh(x)

Solution
0 0

The given vectors are solutions of a system X' = AX. Determine whether the vectors form a fundamental set on the interval (-inf, inf). X1 = ( 1, -1 )e^t, X2 = (3 5)e^t + (8 -8)te^t Yes, since the set X1, X2 is linearly independent for -inf < t < inf. Yes, since the set X1, X2 is linearly dependent for -inf < t < inf. No, since the set X1, X2 is linearly independent for -inf < t < inf. No, since the set X1, X2 is linearly dependent for -inf < t < inf. There is not enough information.

Solution
1 0

X1 = (1 -2 4) + t(1 2 2), X2 = (1 -2 4), X3 = (5 -10 20) + t(4 8 8) The given vectors are solutions of a system X' = AX. Determine whether the vectors form a fundamental set on the interval (-inf, inf). Yes, since the set X1, X2, X3 is linearly independent for -inf < t < inf. Yes, since the set X1, X2, X3 is linearly dependent for -inf < t < inf. No, since the set X1, X2, X3 is linearly independent for -inf < t < inf. No, since the set X1, X2, X3 is linearly dependent for -inf < t < inf. There is not enough information.

Solution
1 0