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.
-
Write the system of equations in matrix form, AX = B.
- Obtain the determinant of A.
- Obtain A1 by substituting B in Column 1 of A. Find the determinant of A1.
- Obtain det(A2) in similar fashion.
- Obtain x = det(A1) / det(A).
- Obtain y = det(A2) / det(A).
- 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.
-
Find the inverse of A.
- Obtain x and y by pre-multiplying
A-1 by B.
B. Consider the following system of equations:
(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.
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