Solved: In each of 5 through 7, determine whether the given functions are linearly

Chapter 4, Problem 7

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QUESTION:

In each of 5 through 7, determine whether the given functions are linearly dependent or linearly independent. If they are linearly dependent, find a linear relation among them. f1(t) = 2t 3, f2(t) = t2 + 1, f3(t) = 2t2 t, f4(t) = t2 + t + 1

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QUESTION:

In each of 5 through 7, determine whether the given functions are linearly dependent or linearly independent. If they are linearly dependent, find a linear relation among them. f1(t) = 2t 3, f2(t) = t2 + 1, f3(t) = 2t2 t, f4(t) = t2 + t + 1

ANSWER:

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According to the theorem of Linear Dependence and Independence, the functions , , , and  are linearly dependant on an interval  if a set of constants ,  and all are not equal to zeros such that  for all  in . Therefore,

                                                       

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