Final answer:
To find constants for linearly dependent functions, use a linear combination of the functions multiplied by respective constants to set up an equation that sums to zero, then solve for the constants, ensuring they are not all zero.
Step-by-step explanation:
The question asks to find constants for a set of linearly dependent functions such that a certain relation holds true. When functions are linearly dependent, there exist constants, not all zero, that can be multiplied with each of these functions to create an equation that sums to zero. To find these constants, one can use the method of linear combination, ensuring that the sum of the multiplied functions is zero. Here is how you might approach it:
- Write down all the functions given as part of a equation set equal to zero.
- Assign a constant to each function (let's call them a, b, c, etc.).
- Set up the equation to reflect the linear combination of these functions multiplied by their respective constants equaling zero.
- Solve the system of equations to find the values of the constants.
Remember that you're looking for a nontrivial solution, so not all constants should be zero.