Homework SourseState whether the statement is true or false If true or fals
State whether the statement is true or false. If true or false, state reason in 1 paragraph (Give an example)
A set of functions is linearly dependent on an interval if a least one function can be expressed as a linear combination of the remaining functions.
For the given functions f1(x) = ex+2 and f2(x) = ex-3 .
We can rewrite f2(x) = ex-3 = ex+2-5 = ex+2 .e-5 = f1(x).e-5
As we notice, f2 is expressed as a linear combination of f1, therefore the two functions are linearly dependent.
We can also use the Wronskian of these functions to prove the linearly dependence. In this case the determinant needs to be equal to zero.
A set of functions is linearly dependent on an interval if a least one function can be expressed as a linear combination of the remaining functions.
For the given functions f1(x) = ex+2 and f2(x) = ex-3 .
We can rewrite f2(x) = ex-3 = ex+2-5 = ex+2 .e-5 = f1(x).e-5
As we notice, f2 is expressed as a linear combination of f1, therefore the two functions are linearly dependent.
We can also use the Wronskian of these functions to prove the linearly dependence. In this case the determinant needs to be equal to zero.
Solution
true
