Problems 1. (30 points) Consider the following system of linear equations. as 3:12 = fl 3d1 + 5.12 243 2 f2 2d2 + 2'13 = Is (a) Rewrite the system of equations in the form [A]{d} = {f} in which [A] is a square 1111 f1 matrix, and {d} = d2 and {f} = f2 are column vectors. Determine matrix [A] . d3 f3 (b) If d1 = 1, d2 = 2, and d3 = 3, nd the values of f1, f2, and f3. (c) Find the determinant of [A] Based on your result, if you were given )3, f2, and f3, would a unique solution exist for d1, 12, and 033'? (d) If d1 = 0, express the system of equations in the form [B] {:2} = {f} Determine 3 3 matrix [B]. (e) Matrix [B] can be obtained by eliminating a row and a column of matrix [A]. Which row and column of matrix [A] should be eliminated to obtain matrix [B]? (E) Find the determinant of matrix [B]. (g) If d1 = 0, f2 = 2, and f3 = 3, solve [B] {:2} = {1:2} for values of d2, :13. Then nd 3 3 the value of f1