Homework SoursePlease state whether or not the statement below is true or f
Please state whether or not the statement below is true or false. If true or false give reason why, in one paragraph.
The set of functions is linearly independent on I if and only if W(f, g) ? 0 for every x in the interval. The Wronskian determinant for the set of functions f1(x) = e^x + 2 , f2(x) = e^x - 3 on (- ?, ? ) is equal to 0. Thus, the Wronskian is zero and the two functions are linearly dependent.
The set of functions is linearly independent on I if and only if W(f, g) ? 0 for every x in the interval. The Wronskian determinant for the set of functions f1(x) = e^x + 2 , f2(x) = e^x - 3 on (- ?, ? ) is equal to 0. Thus, the Wronskian is zero and the two functions are linearly dependent.
Solution
True, because according to the defination they are independent if, W(f,g) is not equal to 0, but here they are equal to 0, so the functions are dependent.
