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# Seven Problems on Determinants, Cramer's Rule and Matrices

Seven practice problems are in the attached file.

1. Use Cramer's rule to solve the system

x + y -z = -1
2x - 2y + 3z = -12
X + y - 4z = 13

Solution set is

2. Evaluate the determinate
5 0 0
1 -3 1
1 2 4

3. Use Cramer's rule to solve the system or to determine if it is inconsistent(I) or dependant(D)

-2x - 5y = -7
-8x - 20y = -28

The solution set is
The system is either I or D

4. Use Cramer's rule to solve the system or to determine if it is inconsistent(I) or dependant(D)
x + y = 5
x - y = 1

The solution set is
The system is either I or D

5. a) Write the linear system as a matrix equation in the form AX=B
b) Solve the system using the inverse that is given for the coefficient matrix

X - 4y - 4z = -4
X + 2y - 4z = -10 A-1 1/3 0 2/3
X + 2y + 2z = 8 -1/6 1/6 0
0 -1/6 1/6

AX=B __ __ __ __ __
__ __ __ __ = __
__ __ __ __ __

The solution set is __ __ __

6. a) Write the linear system as a matrix equation in the form AX=B
b) Solve the system using the inverse that is given for the coefficient matrix

-2/3 0 -1/3
x + y +z = -2 1/3 -1/3 0
-x - 2y + z = 10 A-1 0 1/3 -1/3
-x - 2y - 2z = -2

AX=B __ __ __ __ __
__ __ __ __ = __
__ __ __ __ __

The solution set is __ __ __

7. a) Write the linear system as a matrix equation in the form AX=B
b) Solve the system using the inverse that is given for the coefficient matrix

X - y - z =0 3 3 1
-2y - z = 1 A-1 4 -4 -1
4x = 3y = 2 -8 7 2

AX=B __ __ __ __ __
__ __ __ __ = __
__ __ __ __ __

The solution set is __ __ __

#### Solution Summary

Seven practice problems on Determinants, Cramers's Rule and Matrices fully solved.

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