Exercise Set 5
Cramer's Rule

A. Consider the following system of equations:

(1)   5x = 52 + 2y

(2)   4y - 100 + 3x = 0

1. Solve equations (1) and (2) for x and y using Cramer's Rule.

1. Write the system of equations in matrix form, AX = B.
2. Obtain the determinant of A.
3. Obtain A1 by substituting B in Column 1 of A. Find the determinant of A1.
4. Obtain det(A2) in similar fashion.
5. Obtain x = det(A1) / det(A).
6. Obtain y = det(A2) / det(A).
7. Confirm the accuracy of your results by substituting for x and y in (1) and (2).

2. Solve equations (1) and (2) using the inverse of A.

1. Find the inverse of A.
2. Obtain x and y by pre-multiplying A^-1 by B.

(1)   4x + 3y - 2z - 7 = 0

(2)   x + y = 5

(3)   3x - 4 = -z

1. Use Cramer's Rule to solve equations (1) - (3) for x, y and z.

2. Solve equations (1) - (3) using A^-1.