Final answer:
To determine if a set of vectors is linearly independent, set up an equation and solve for the constants. If the only solution is all the constants being zero, the vectors are linearly independent.
Step-by-step explanation:
In order to determine if a set of vectors is linearly independent, we need to evaluate whether any one of the vectors in the set can be expressed as a linear combination of the others. To do this, we set up an equation:
c1v1 + c2v2 + c3v3 + ... + cnvn = 0
where c1, c2, c3, ..., cn are constants and v1, v2, v3, ..., vn are the vectors in the set. If the only solution to this equation is c1 = c2 = c3 = ... = cn = 0, then the vectors are linearly independent. If there are other non-zero solutions, then the vectors are linearly dependent.
By substituting the values of the vectors into the equation and solving, you can determine if the vectors are linearly independent.