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Solved: In each of 5 through 7, determine whether the given functions are linearly
Chapter 4, Problem 7(choose chapter or problem)
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
Questions & Answers
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:Step 1 of 2
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,