For any 2 x 2 matrix A = a12 we define the trace of A, tr A, to a21 a 22 be tr A = all + a22. Consider V = {A : A is 2 x 2 real matrix with tr A = 0}, which is a linear subspace of R2x2. Every matrix in V is of the form a C -a , where a, b, c can be any real numbers. We can show that is a basis for V. Note that - a = aB1 + bB2 + cB3. (You don't need to prove anything stated above and you can view them as facts.) Answer the following question. Question: Is the following set S linearly dependent in V? You may use their coordinate vectors relative to the basis B. Justify your answer and show all your steps. (You cannot only write down the answer. )