Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use s1, s2, and s3, respectively, for the vectors in the set.) S = {(3, 2), (−1, 1), (4, 0)}

The solution is explained below

Explanation

What you want to do here is use Gauss-Jordan elimination to find the reduced row echelon form. Then you'll see that there is at least one column without a leading 1. Then your first column represents a₁, your second a₂, and 3rd is a₃. Whichever column(s) doesn't have a leading 1, you can set that variable equation to an arbitrary value.

Then solve for a₁ and a₂ in terms of t. For the matrix, you'd have a₁=0−3t=−3t, a₂=0−t=−t and a₃=t. Whatever you get at this point will be the general solution.

thermal energy is the answer