# 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.