Use Cramer’s rule to solve the system. 2x + 4y – z = 32 x – 2y + 2z = 5 5x + y + z = 20


Find the products AB and BA to determine whether B is the multiplicative inverse of A.
A = , B =


Evaluate the determinant.


Evaluate the determinant.


Solve the system of equations using matrices. Use GaussJordan elimination.
3x – 7 – 7z = 7






Determinants are used to show that three points lie on the same line (are collinear). If
= 0, then the points ( x_{1}, y_{1}), ( x_{2}, y_{2}), and ( x_{3}, y_{3}) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points (2, 1), (0, 9), (6, 21) and collinear? 

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
x + y + z = 9 

Let B = [1 3 6 3]. Find 4B.


Find the inverse of the matrix, if possible.
A = 

Find the product AB, if possible.
A = , B = 



Use Cramer’s rule to determine if the system is inconsistent system or contains dependent equations.
2x + 7 = 8


Solve the system of equations using matrices. Use Gaussian elimination with backsubstitution.
3x + 5y – 2w = 13


Find the products AB and BA to determine whether B is the multiplicative inverse of A.
A = , B =


Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
3x – 2y + 2z – w = 2 

Give the order of the matrix, and identify the given element of the matrix.
; a12


Let A = and B = . Find A – 3B.



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