Problem 1: Cramer's Rule (10 points) Consider the linear system A * = b, represented by | 0 3 0 |x2 - : where a is a constant. allx3] a. The determinant of A is: b. We can apply Cramer's rule only if the constant a satisfies: c. Cramer's rule states that the solutions are the simple fractions: x1 |A21 |A31 X 2 X3 Write out each of the three matrices A1, A2 and A3. A1 = A2 = A3 c. One of the determinants is given for you. Find the missing determinants | A, | and |A2l. |All = |A21 = |A31 = 6a d. Write out the missing solutions by applying Cramer's formula. The third is given for you. X1 = X2 = X3 = -2 1] [x 1] e. Consider the special case where a = 0. The system now simplifies to 3 0 X2 - 6 . The number of solutions for this new system is infinite since X3 is a free variable. Write all the solutions in vector parametric form. Hint: Row reduce! Particular...... Homogeneous Ix X2 X3