Consider the linear system x1 3x2 x1 + 4x = 2 3x3 = 1 x2 + 5x3 = 0 - (a) Write down the coefficient matrix A and compute its determinant. (b) Let a,, i = 1,2,3 denote the row-vectors of A, ordered from top to bottom. Compute the vector cross-products a a3, and a2 a3, then the scalar triple-products a (a2 x a3) and a2 (a1 x a3). . (c) Using the results obtained in (b), find vectors u and v that satisfy the matrix-vector equations Aue and Av = e2 where e ,1 1,2,3 denote the standard coordinate vectors in R. Then find real coefficients A and so that the linear combination X = \u + v satisfies the above system of equations AX= b where b = (2,1,0). (d) Is this solution unique? Explain your answer in terms of the solution space So for the corresponding homogeneous system AX = 0.